Tootfinder

Reflexive dg categories in algebra and topology
Matt Booth, Isambard Goodbody, Sebastian Opper
https://arxiv.org/abs/2506.11213 https://

Reflexive dg categories in algebra and topology
Reflexive dg categories were introduced by Kuznetsov and Shinder to abstract the duality between bounded and perfect derived categories. In particular this duality relates their Hochschild cohomologies, autoequivalence groups, and semiorthogonal decompositions. We establish reflexivity in a variety of settings including affine schemes, simple-minded collections, chain and cochain dg algebras of topological spaces, Ginzburg dg algebras, and Fukaya categories of cotangent bundles and surfaces as …

Duality-symmetric D3-brane action with twisted self-dual 2-form doublet
Pichet Vanichchapongjaroen
https://arxiv.org/abs/2506.07219 https://

Duality-symmetric D3-brane action with twisted self-dual 2-form doublet
In this paper we apply the Sen formulation, which is originally developed for chiral form fields, to construct non-linear duality-symmetric actions in four dimensions. In particular, the duality-symmetric D3-brane action coupled to the type IIB supergravity background is constructed in the Sen formulation. Key features of the Sen formulation are also present in the duality-symmetric actions. For example, there are unphysical fields with the wrong sign of kinetic terms. These fields are uncouple…

Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings
Sanjit Bhowmick, Kuntal Deka, Alexandre Fotue Tabue, Edgar Mart\'inez-Moro
https://arxiv.org/abs/2506.10381

Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings
This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are free modules. Moreover, we present a necessary and sufficient condition for a pair of additive cyclic codes over a finite commutative ring to form an additive complementary pair. Finally, we construct a complementary pair of additive cyclic codes over a finite…

This https://arxiv.org/abs/2309.14542 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Trace Maps on Rigid Stein Spaces
We provide a relative version of the trace map from the work of Beyer, which can be associated to any finite tale morphism $X \to Y$ of smooth rigid Stein spaces and which then relates the Serre duality on $X$ with the Serre duality on $Y$. Furthermore, we consider the behaviour of any rigid Stein space under (completed) base change to any complete extension field and deduce a commutative diagram relating Serre duality over the base field with the Serre duality over the extension field.

Introducing a vertex polynomial invariant for embedded graphs
Qi Yan, Qingying Deng, Metrose Metsidik
https://arxiv.org/abs/2506.07522 https://

Introducing a vertex polynomial invariant for embedded graphs
The ribbon group action extends geometric duality and Petrie duality by defining two embedded graphs as twisted duals precisely when they lie within the same orbit under this group action. Twisted duality yields numerous novel properties of fundamental graph polynomials. In this paper, we resolve a problem raised by Ellis-Monaghan and Moffatt [Trans. Amer. Math. Soc. 364 (2012), 1529--1569] for vertex counts by introducing the vertex polynomial: a generating function quantifying vertex distribu…

Composite Optimization with Indicator Functions: Stationary Duality and a Semismooth Newton Method
Penghe Zhang, Naihua Xiu, Houduo Qi
https://arxiv.org/abs/2506.08374

Composite Optimization with Indicator Functions: Stationary Duality and a Semismooth Newton Method
Indicator functions of taking values of zero or one are essential to numerous applications in machine learning and statistics. The corresponding primal optimization model has been researched in several recent works. However, its dual problem is a more challenging topic that has not been well addressed. One possible reason is that the Fenchel conjugate of any indicator function is finite only at the origin. This work aims to explore the dual optimization for the sum of a strongly convex function…

$x-y$ swap for $(2,2p 1)$ minimal string
Aleksandr Artemev
https://arxiv.org/abs/2506.09222 https://arxiv.org/pdf/2506.09222

$x-y$ swap for $(2,2p+1)$ minimal string
We continue the study of 2D gravity -- ``matrix model'' duality on the example of $(2,2p+1)$ minimal string. We propose a reformulation of the duality, related to a more conventional one by ``$x-y$ swap'' in the language of topological recursion. This formulation elucidates some conceptual and technical difficulties in the dictionary of the duality and relation to other examples. In particular, it allows to circumvent the necessity to use ``resonance transformations'', that were previously intr…

The Bisognano-Wichmann property for non-unitary Wightman conformal field theories
James E. Tener
https://arxiv.org/abs/2506.10625 https://

The Bisognano-Wichmann property for non-unitary Wightman conformal field theories
The Bisognano-Wichmann and Haag duality properties for algebraic quantum field theories are often studied using the powerful tools of Tomita-Takesaki modular theory for nets of operator algebras. In this article, we study analogous properties of nets of algebras generated by smeared Wightman fields, for potentially non-unitary theories. In light of recent work constructing Wightman field theories for (non-unitary) Möbius vertex algebras, we obtain a broadly applicable non-unitary version of th…

Understanding Flow Behaviors of Supercooled Liquids by Embodying Solid-Liquid Duality at Particle Level
Dong-Xu Yu, Ke-Qi Zeng, Zhe Wang
https://arxiv.org/abs/2506.03818

Understanding Flow Behaviors of Supercooled Liquids by Embodying Solid-Liquid Duality at Particle Level
Supercooled liquids exhibit intricate flow behaviors, which progressively become nonlinear as flow rate increases. Conceptually, this complexity can be understood by the solid-liquid duality in Maxwell's understanding of materials' response to external load. Nevertheless, the microscopic foundation of this duality in supercooled liquids remains elusive, thereby impeding the modeling of flow behaviors from a microscopic viewpoint. The existence of dynamic heterogeneity adds to this difficulty. T…

This https://arxiv.org/abs/2505.00858 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

Duality on the Thermodynamics of the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange Scheme
This study investigates a duality approach to information leak detection in the generalized Kirchhoff-Law-Johnson-Noise secure key exchange scheme proposed by Vadai, Mingesz, and Gingl (VMG-KLJN). While previous work by Chamon and Kish sampled voltages at zero-current instances, this research explores sampling currents at zero-voltage crossings. The objective is to determine if this dual approach can reveal information leaks in non-equilibrium KLJN systems. Results indicate that the duality met…

Three approaches to the Howe duality between quantum general linear supergroups
Li Luo, Xirui Yu, Zhongguo Zhou
https://arxiv.org/abs/2506.01613 https://…

Three approaches to the Howe duality between quantum general linear supergroups
The Howe duality between quantum general linear supergroups was firstly established by Y. Zhang via quantum coordinate superalgebras. In this paper, we provide two other approaches to this Howe duality. One is constructed by quantum differential operators, while the other is based on the Beilinson-Lusztig-MacPherson realization of $U_q(\mathfrak{gl}_{m|n})$. Moreover, we show that these three approaches are equivalent by giving their action formulas explicitly.

Expansion-contraction duality breaking in a Planck-scale sensitive cosmological quantum simulator
S. Mahesh Chandran, Uwe R. Fischer
https://arxiv.org/abs/2506.02719

Expansion-contraction duality breaking in a Planck-scale sensitive cosmological quantum simulator
We propose the experimental simulation of cosmological perturbations governed by a Planck-scale induced Lorentz violating dispersion, aimed at distinguishing between early-universe models with similar power spectra. Employing a novel variant of the scaling approach for the evolution of a Bose-Einstein condensate with both contact and dipolar interactions, we show that scale invariance, and in turn, the duality of the power spectrum is broken at large momenta for an inflating gas, and at small m…

$q$-deformed Howe duality for orthosymplectic Lie superalgebras
Jeong Bae, Jae-Hoon Kwon
https://arxiv.org/abs/2506.05959 https://arx…

$q$-deformed Howe duality for orthosymplectic Lie superalgebras
We give a $q$-analogue of Howe duality associated to a pair $(\mathfrak{g},G)$, where $\mathfrak{g}$ is an orthosymplectic Lie superalgebra and $G=O_\ell, Sp_{2\ell}$. We define explicitly a commuting action of a quantized enveloping algebra of $\mathfrak{g}$ and the $\imath$quantum group of $\mathfrak{so}_\ell, \mathfrak{sp}_{2\ell}$ on a $q$-deformed supersymmetric space, and describe its semisimple decomposition whose classical limit recovers the $(\mathfrak{g},G)$-duality. As special cases,…

This https://arxiv.org/abs/2506.01348 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Distributionally Robust Learning in Survival Analysis
We introduce an innovative approach that incorporates a Distributionally Robust Learning (DRL) approach into Cox regression to enhance the robustness and accuracy of survival predictions. By formulating a DRL framework with a Wasserstein distance-based ambiguity set, we develop a variant Cox model that is less sensitive to assumptions about the underlying data distribution and more resilient to model misspecification and data perturbations. By leveraging Wasserstein duality, we reformulate the …

A duality between surface charge and work function in scanning Kelvin probe microscopy
Isaac C. D. Lenton, Felix Pertl, Lubuna Shafeek, Scott R. Waitukaitis
https://arxiv.org/abs/2506.07187

A duality between surface charge and work function in scanning Kelvin probe microscopy
Scanning Kelvin probe microscopy (SKPM) is a powerful technique for macroscopic imaging of the electrostatic potential above a surface. Though most often used to image work-function variations of conductive surfaces, it can also be used to probe the surface charge on insulating surfaces. In both cases, relating the measured potential to the underlying signal is non-trivial. Here, we derive general relationships between the measured SKPM voltage and the underlying source, revealing either can be…

Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new/
[1/1]:
Poincar\'e duality for loop spaces
https://

Simplicial volume via foliated simplices and duality
Filippo Sarti
https://arxiv.org/abs/2506.02962 https://arxiv.org/pdf/2506.02962

Simplicial volume via foliated simplices and duality
Let $M$ be an aspherical oriented closed connected manifold with universal cover $\widetilde{M}\to M$ and let $Γ=π_1(M)\curvearrowright (X,μ)$ be a measure preserving action on a standard Borel probability space. We consider singular foliated simplices on the measured foliation $Γ\backslash(\widetilde{M}\times X)$ defined by Sauer and we compare the \emph{real singular foliated homology} with classic singular homology. We introduce a notion of \emph{foliated fundamental class} and we prove …

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles
Dongzhe Zheng
https://arxiv.org/abs/2506.00728

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles
This paper develops a mirror symmetry theory of Spencer cohomology within the geometric framework of constrained systems on principal bundles, revealing deep symmetric structures in constraint geometry. Based on compatible pairs $(D,λ)$ under strong transversality conditions, we construct a systematic family of mirror transformations: from basic sign mirrors $λ\mapsto -λ$ to general automorphism-induced mirrors $λ\mapsto (dϕ)^*(λ)$. Our core result proves that these transformations preser…

Position of $L(X, Y)$ in $Lip_0(X, Y)$
Anil Kumar Karn, Arindam Mandal
https://arxiv.org/abs/2506.09324 https://arxiv.org/pdf/2506.09…

Position of $L(X, Y)$ in $Lip_0(X, Y)$
We prove that $L(X,Y)$ is complemented in $Lip_0(X, Y)$ (via a norm-one projection) provided that $Y$ is a dual space. Next, we introduce a vector-valued Lipschitz-free space $F_Y(X)$, a linear contraction $β_X^Y: F_Y(X) \to Y$ and prove that the quotient space ${Lip_{0}(X, Y)}/{L(X, Y) }$ is isometrically isomorphic to $L(\ker(β_X^Y), Y)$ whenever $Y$ is injective. We also consider a $Y$-valued duality pairing between $Lip_0(X, Y)$ and $F_Y(X)$ and obtain a necessary and sufficient condition…

This https://arxiv.org/abs/2501.03460 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

K-theoretic Tate-Poitou duality at prime 2
We extend the result of Blumberg and Mandell on K-theoretic Tate-Poitou duality at odd primes which serves as a spectral refinement of the classical arithmetic Tate-Poitou duality. The duality is formulated for the $K(1)$-localized algebraic K-theory of the ring of $p$-integers in a number field and its completion using the $\mathbb{Z}_p$-Anderson duality. This paper completes the picture by addressing the prime 2, where the real embeddings of number fields introduce extra complexities. As an a…

$d$-Wave Flat Fermi Surface in Altermagnets Enables Maximum Charge-to-Spin Conversion
Junwen Lai, Tianye Yu, Peitao Liu, Long Liu, Guozhong Xing, Xing-Qiu Chen, Yan Sun
https://arxiv.org/abs/2506.07703

$d$-Wave Flat Fermi Surface in Altermagnets Enables Maximum Charge-to-Spin Conversion
Altermagnets combine antiferromagnetic order with ferromagnet-like spin splitting, a duality that unlocks ultrafast spin-dependent responses. This unique property creates unprecedented opportunities for spin-current generation, overcoming the intrinsic limitations of conventional spin-transfer and spin-orbit torque approaches in magnetic memory technologies. Here, we establish a fundamental relationship between Fermi surface geometry and time-reversal-odd ($\mathcal{T}$-odd) spin currents in al…

Residuality Theory: A Rebellious Take on Building Systems That Actually Survive
#resiliency

This https://arxiv.org/abs/2502.14032 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Critical theories connecting gapped phases with $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry from the duality web
We use the ideas behind the duality web to construct numerous conformal field theories mediating the phase transitions between various symmetry broken and topological phases. In particular we obtain the full field theory version of the Kennedy Tasaki transformation, mapping a gapless theory mediating a topological phase transition of symmetry protected topological orders to a standard symmetry breaking one in a 1+1 dimensional $\mathbb{Z}_2 \times \mathbb{Z}_2$ gauge theory. When we consider al…

Replaced article(s) found for physics.hist-ph. https://arxiv.org/list/physics.hist-ph/new/
[1/1]:
The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gr...

d-Boolean algebras and their bitopological representation
Hang Yang, Dexue Zhang
https://arxiv.org/abs/2505.17806 https://arxiv.org/p…

d-Boolean algebras and their bitopological representation
We present a Stone duality for bitopological spaces in analogy to the duality between Stone spaces and Boolean algebras, in the same vein as the duality between d-sober bitopological spaces and spatial d-frames established by Jung and Moshier. Precisely, we introduce the notion of d-Boolean algebras and prove that the category of such algebras is dually equivalent to the category of Stone bitopological spaces, which are compact and zero-dimensional bitopological spaces satisfying the T0 separat…

Angular $k$-uniformity and the Hyperinvariance of Holographic Codes
Wanli Cheng
https://arxiv.org/abs/2506.06577 https://arxiv.org/pd…

Angular $k$-uniformity and the Hyperinvariance of Holographic Codes
Holographic quantum error-correcting codes, often realized through tensor network architectures, have emerged as compelling toy models for exploring bulk-boundary duality in AdS-CFT. By encoding bulk information into highly entangled boundary degrees of freedom, they capture key features of holography such as subregion duality, operator reconstruction, and complementary recovery. Among them, hyperinvariant tensor networks-characterized by the inclusion of edge tensors and the enforcement of mul…

Tug-of-war between idiom's figurative and literal meanings in LLMs
Soyoung Oh, Xinting Huang, Mathis Pink, Michael Hahn, Vera Demberg
https://arxiv.org/abs/2506.01723

Tug-of-war between idiom's figurative and literal meanings in LLMs
Idioms present a unique challenge for language models due to their non-compositional figurative meanings, which often strongly diverge from the idiom's literal interpretation. This duality requires a model to learn representing and deciding between the two meanings to interpret an idiom in a figurative sense, or literally. In this paper, we employ tools from mechanistic interpretability to trace how a large pretrained causal transformer (LLama3.2-1B-base) deals with this ambiguity. We localize …

RSK correspondence for King tableaux with Berele insertion
Masato Kobayashi, Tomoo Matsumura
https://arxiv.org/abs/2506.06951 https://

RSK correspondence for King tableaux with Berele insertion
We establish a bijective RSK correspondence of type C for King tableaux with Berele insertion as a reformulation of Sundaram's correspondence (1986). For its $Q$-symbol, we make use of semistandard oscillating tableaux (SSOT), a new object which Lee (2025) introduced. Further, we show hidden duality of Cauchy identity through RSK correspondences of type A and C. Finally, we prove that the generating function of SSOT is symmetric by constructing a new sort of Bender-Knuth involution.

Replaced article(s) found for physics.class-ph. https://arxiv.org/list/physics.class-ph/new/
[1/1]:
The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gr...

This https://arxiv.org/abs/2504.09447 has been replaced.
initial toot: https://mastoxiv.page/@a…

Unconventional compensated magnetic material LaMn$_2$SbO$_6$
Unconventional magnetism including altermagnetism and unconventional compensated magnetism, characterized by its duality of real-space antiferromagnetic alignment and momentum-space spin splitting, has garnered widespread attention. While altermagnetism has been extensively studied, research on unconventional compensated magnetism remains very rare. In particular, unconventional compensated magnetic materials are only theoretically predicted and have not yet been synthesized experimentally. In …

Off-shell double copy theories in BV
Maor Ben-Shahar, Francesco Bonechi, Maxim Zabzine
https://arxiv.org/abs/2506.09869 https://arxiv…

Off-shell double copy theories in BV
We present a construction of the double copy for gauge theories that exhibit off-shell color-kinematics duality within the Batalin-Vilkovitsky (BV) formalism. As illustrative examples, we consider the double copies of Chern-Simons theory, four-dimensional BF theory, and two-dimensional Yang-Mills theory, and we discuss possible gravity interpretations for these cases. We formalize the construction and demonstrate that Kodaira-Spencer gravity, Kähler gravity, and their generalizations, fit natu…

This https://arxiv.org/abs/2501.04357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Generators of top cohomology
Let $R$ be a commutative noetherian ring and $f: X \to \mathrm{Spec} R$ a proper smooth morphism, of relative dimension $n$. From Hartshorne, Residues and Duality, Springer, 1966, one knows that the trace map $\mathrm{Tr}_f : \mathrm{H}^n(X, ω_{X/R}) \to R$ is an isomorphism when $f$ has geometrically connected fibres. We construct an exact sequence that generates $\mathrm{Ext}_X^n(\mathcal{O}_X, ω_{X/R}) = \mathrm{H}^n(X, ω_{X/R})$ as an $R$-module in the following cases: (1) when $R$ is…

This https://arxiv.org/abs/2505.21677 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

What happens when generative AI models train recursively on each others' generated outputs?
The internet is full of AI-generated content while also serving as a common source of training data for generative AI (genAI) models. This duality raises the possibility that future genAI models may be trained on other models' generated outputs. Prior work has studied consequences of models training on their own generated outputs, but limited work has considered what happens if models ingest content produced by other models. Given society's increasing dependence on genAI tools, understanding do…

This https://arxiv.org/abs/2411.15932 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sobolev $(p,q)$-extension operators and Neumann eigenvalues
In this article, we study $(p,q)$-extension operators of Sobolev spaces, based on the duality of composition operators within these spaces. We construct Sobolev extension operators in Hölder singular domains using corresponding reflections. In addition, we use the $(p,q)$-extension operators to estimate non-linear Neumann eigenvalues.

This https://arxiv.org/abs/2409.10612 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Duality-preserving deformation of 3+1d lattice $\mathbb Z_2$ gauge theory with exact gapped ground states
We propose and analyze a deformation of the 3+1d lattice $\mathbb Z_2$ gauge theory that preserves the non-invertible Wegner duality symmetry at the self-dual point. We identify a frustration-free point along this deformation where there are nine exactly degenerate ground states (on a periodic cubic lattice) even at finite volume. One of these ground states is a trivial product state and the rest are the topologically-ordered ground states of the 3+1d toric code. We also prove that the frustrat…

Shellings of Tropical Hypersurfaces
George Balla, Michael Joswig, Lena Weis
https://arxiv.org/abs/2506.07241 https://arxiv.org/pdf/25…

Shellings of Tropical Hypersurfaces
The shellability of the boundary complex of an unbounded polyhedron is investigated. To this end, it is necessary to pass to a suitable compactification, e.g., by one point. This observation can be exploited to prove that any tropical hypersurface is shellable. Under the hood there is a subtle interplay between the duality of polyhedral complexes and their shellability. Translated into discrete Morse theory, that interplay entails that the tight span of an arbitrary regular subdivision is colla…

First-Passage-Time Asymmetry for Biased Run-and-Tumble Processes
Yonathan Sarmiento, Benjamin Walter, Debraj Das, Samvit Mahapatra, \'Edgar Rold\'an, Rosemary J. Harris
https://arxiv.org/abs/2505.24483

First-Passage-Time Asymmetry for Biased Run-and-Tumble Processes
We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no symmetry between distributions of first-passage times to symmetric barriers positioned in and against the bias direction; however, we give conditions for such a duality to be restored asymptotically (in the limit of a large barrier distance) and highlight connec…

This https://arxiv.org/abs/2412.05927 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Abstract categorical residues and Calabi-Yau structures
Inspired by the simple fact that a compact n-dimensional manifold-with-boundary which satisfies Poincaré-Lefschetz duality of dimension n has a boundary which itself satisfies Poincaré duality of dimension n, we show that the categorical formal punctured neighborhood of infinity, a canonical categorical construction associated to every $A_{\infty}$ category, has a weak proper Calabi-Yau structure of dimension n-1 whenever the original $A_{\infty}$ category admits a weak smooth Calabi-Yau stru…

This https://arxiv.org/abs/2501.14263 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Anticipated backward stochastic Volterra integral equations and their applications to nonzero-sum stochastic differential games
In [J. Wen, Y. Shi, Stat. Probab. Lett. 156 (2020) 108599] the authors first introduced a kind of anticipated backward stochastic Volterra integral equations (anticipated BSVIEs, for short). By virtue of the duality principle, it is found in this paper that the anticipated BSVIEs can be applied to the study of stochastic differential games. For this, in this paper we deeply investigate a more general class of anticipated BSVIEs whose generator includes both pointwise time-advanced functions and…

Howe duality for the dual pair $\left(\mathfrak{spo}(2n|1)\,, \mathfrak{osp}(2|2)\right)$
Roman Lavicka, Allan Merino
https://arxiv.org/abs/2506.04075 http…

Howe duality for the dual pair $\left(\mathfrak{spo}(2n|1)\,, \mathfrak{osp}(2|2)\right)$
The goal of our work is to study the decomposition of the joint action of $\mathfrak{g} = \mathfrak{spo}(2n|1)$ and $\mathfrak{g}' = \mathfrak{osp}(2|2)$ on the supersymmetric algebra S = S($\mathbb{C}^{2n|1} \otimes \mathbb{C}^{1|1}$). As proved by Merino and Salmasian, we have a one-to-one correspondence between irreducible representations of $\mathfrak{g}$ and $\mathfrak{g}'$ appearing as subrepresentations of S. In this paper, we obtained an explicit description of the h…

This https://arxiv.org/abs/2505.10439 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Interpolating Feigin-Frenkel Duality at the Critical Level to Matrices of Complex Size
In this paper, we extend Feigin-Frenkel duality at the critical level to the setting of complex rank. This is accomplished by considering the center of a vertex algebra in Deligne's interpolating categories, along with Feigin's Lie algebras of complex rank, $\mathfrak{gl}_λ$ and $\mathfrak{po}_λ$. More precisely, we define the universal affine vertex algebras associated with Lie algebras in $\underline{\mathrm{Re}}\mathrm{p}(\mathrm{GL}_α,\mathbb{F})$, $\underline{\mathrm{Re}}\mathrm{p}(\mat…

Mizohata-Takeuchi inequalities for orthonormal systems
Jonathan Bennett, Neal Bez, Susana Gutierrez, Shohei Nakamura, Itamar Oliveira
https://arxiv.org/abs/2506.03783

Mizohata-Takeuchi inequalities for orthonormal systems
We establish some weighted $L^2$ inequalities for Fourier extension operators in the setting of orthonormal systems. In the process we develop a direct approach to such inequalities based on generalised Wigner distributions, complementing the Schatten duality approach that is prevalent in the wider context of estimates for such orthonormal systems. Our results are set within a broader family of tentatively suggested ($L^p$) inequalities of Mizohata-Takeuchi type. For $p$ a power of two at least…

This https://arxiv.org/abs/2405.20907 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Muckenhoupt condition
The goal of this paper is to unify the theory of weights beyond the setting of weighted Lebesgue spaces in the general setting of quasi-Banach function spaces. We prove new characterizations for the boundedness of singular integrals, pose several conjectures, and prove partial results related to the duality of the Hardy-Littlewood maximal operator. Furthermore, we give an overview of the theory applied to weighted variable Lebesgue, Morrey, and Musielak-Orlicz spaces.

Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law
Sampurna Karmakar, Amulya Ratnakar, Sourin Das
https://arxiv.org/abs/2506.01930

Statistical Interaction Driven Thermoelectricity and Violation of Wiedemann-Franz Law
Quantum transport anomalies in systems obeying Haldane-Wu fractional exclusion statistics, characterized by the statistical interactions parameter $g$ are investigated. We identify particle-hole symmetry breaking of the Haldane-Wu distribution function via its deviations of the maximum entropy ($\mathcal{S}_{g}^{max}$), evaluated at the chemical potential, from the value ${k_B} \ln 2$ (a value that holds only at the free fermion limit, $g=1$). A duality relation, $g\,\mathcal{S}_{g}^{max}=\math…

Effect of non-conformal deformation on the gapped quasinormal modes and its holographic implications
Ashis Saha, Sunandan Gangopadhyay
https://arxiv.org/abs/2506.09431

Effect of non-conformal deformation on the gapped quasinormal modes and its holographic implications
The spectral curve of quasinormal modes for a massive real scalar field in the background of a non-conformal black brane geometry has been obtained by utilizing a Frobenius type near-horizon expansion. The gauge/gravity duality maps this to the computation of spectral curve of a scalar operator $\mathcal{O}_ϕ$ with conformal dimension $Δ_ϕ$ for a large-$N$ conformal field theory with irrelevant type non-conformal deformation. In this context, non-conformality has been holographically introdu…

This https://arxiv.org/abs/2312.02943 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qfi…

Striking the Balance: Life Insurance Timing and Asset Allocation in Financial Planning
This paper investigates the consumption and investment decisions of an individual facing uncertain lifespan and stochastic labor income within a Black-Scholes market framework. A key aspect of our study involves the agent's option to choose when to acquire life insurance for bequest purposes. We examine two scenarios: one with a fixed bequest amount and another with a controlled bequest amount. Applying duality theory and addressing free-boundary problems, we analytically solve both cases, and …

This https://arxiv.org/abs/2407.17567 has been replaced.
initial toot: https://mastoxiv.page/@a…

Fermion-Vortex Interactions in Axion Electrodynamics
A relativistic action for scalar condensate-fermion mixture is considered where both the scalar boson and the fermion fields are coupled to a $U(1)$ gauge field. The dynamics of the gauge field is governed by a linear combination of the Maxwell term, and the Lorentz invariant $\mathbf{E\cdot B}$ term with a constant coefficient $θ$. We obtain an effective action describing an emergent fermion-fermion interaction and fermion-vortex tube interaction by using the particle-string duality, and find…

This https://arxiv.org/abs/2505.07960 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$C^\ast$-categorical prefactorization algebras for superselection sectors and topological order
This paper presents a conceptual and efficient geometric framework to encode the algebraic structures on the category of superselection sectors of an algebraic quantum field theory on the $n$-dimensional lattice $\mathbb{Z}^n$. It is shown that, under certain assumptions which are implied by Haag duality, the monoidal $C^\ast$-categories of localized superselection sectors carry the structure of a locally constant prefactorization algebra over the category of cone-shaped subsets of $\mathbb{Z}^…

This https://arxiv.org/abs/2205.12953 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces
We prove a blow-up formula for the generating series of virtual $χ_y$-genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topological $χ_y$-genera of Göttsche. Our formula is a refinement of one by Vafa-Witten relating to S-duality. We prove the formula simultaneously in the setting of Gieseker stable sheaves on polarised surfaces and also in the setting of framed sheaves on $\mathbb{P}^2$. The proof is based on the blow-up algorithm of N…

This https://arxiv.org/abs/2301.10980 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Beyond scalar quasi-arithmetic means: Quasi-arithmetic averages and quasi-arithmetic mixtures in information geometry
We generalize quasi-arithmetic means beyond scalars by considering the gradient map of a Legendre type real-valued function. The gradient map of a Legendre type function is proven strictly comonotone with a global inverse. It thus yields a generalization of strictly mononotone and differentiable functions generating scalar quasi-arithmetic means. Furthermore, the Legendre transformation gives rise to pairs of dual quasi-arithmetic averages via the convex duality. We study the invariance and equ…

Emergent Holographic Spacetime from Quantum Information
Tadashi Takayanagi
https://arxiv.org/abs/2506.06595 https://arxiv.org/pdf/250…

Emergent Holographic Spacetime from Quantum Information
Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries of gravitational spacetimes. One manifestation is that the entanglement entropy in quantum many-body systems can be calculated from the area of an extremal surface in the corresponding gravitational spacetime. This implies that a gravitational spacetime can em…

This https://arxiv.org/abs/2505.19412 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries
The Cardy-Rabinovici model is a toy model of the lattice $U(1)$ gauge theories to study various oblique confinement states associated with the nonzero $θ$ angles. We reformulate the $2$d version of this model using the modified Villain lattice formalism, and we establish the exact $θ$ periodicity for the Witten effect and the strong-weak duality at the finite lattice spacings. We then study the phase structure of this model based on the duality, symmetry and anomaly, and the perturbative reno…

This https://arxiv.org/abs/2505.15726 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fluctuations of Young diagrams for symplectic groups and semiclassical orthogonal polynomials
Consider an $n\times k$ matrix of i.i.d. Bernoulli random numbers with $p=1/2$. Dual RSK algorithm gives a bijection of this matrix to a pair of Young tableaux of conjugate shape, which is manifestation of skew Howe $GL_{n}\times GL_{k}$-duality. Thus the probability measure on zero-ones matrix leads to the probability measure on Young diagrams proportional to the ratio of the dimension of $GL_{n}\times GL_{k}$-representation and the dimension of the exterior algebra $\bigwedge\left(\mathbb{C}^…

This https://arxiv.org/abs/2408.05103 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Koszul duality for generalised Steinberg representations of $p$-adic groups
Let $G$ be a semisimple group, split over a non-Archimedean field $F$. We prove that the category of modules over the extension algebra of generalised Steinberg representations of $G(F)$ is equivalent to a full subcategory of equivariant perverse sheaves on the variety of Langlands parameters for these representations. Specifically, we establish an equivalence \[ \textbf{Mod}(\text{Ext}_G^\bullet(Σ_λ, Σ_λ)) \simeq \textbf{Per}_{\widehat{G}}^\circ(X_λ), \] where $Σ_λ$ is the direct sum of…

This https://arxiv.org/abs/2409.16330 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On certain $q$-multiple sums
We present outlines of a general method to reach certain kinds of $q$-multiple sum identities. Throughout our exposition, we shall give generalizations to the results given by Dilcher, Prodinger, Fu and Lascoux, Zeng, and Guo and Zhang concerning $q$-series identities related to divisor functions. Our exposition shall also provide a generalization of the duality relation for finite multiple harmonic $q$-series given by Bradley. Utilizing these generalizations, we will also arrive at some new in…

This https://arxiv.org/abs/2506.00120 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Type II RR string fields and exotic diffeomorphisms
We study the theory of massless fields of type II strings arising from the string field theory that uses two string fields, a physical one and an extra one that allows the writing of an action, but whose degrees of freedom ultimately decouple. The mechanism allowing the description of the self-dual five-form of type IIB, anticipated by Sen, is used by the SFT to describe all Ramond-Ramond forms in type IIB and IIA in a manifestly duality-invariant way. We find explicit expressions for the leadi…

This https://arxiv.org/abs/2312.08923 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Topology change and heterotic flux vacua
We investigate the interrelation between topology and Narain T-duality of heterotic flux vacua. We present evidence that all 5 and 4-dimensional Minkowski space heterotic flux backgrounds with 8 supercharges have a locus in the moduli space with a T-dual description in terms of a compactification on the product of a K3 surface with a circle or a torus. A test of this equivalence is provided by calculating the new supersymmetric index on both sides of the duality. We examine the implications of …

This https://arxiv.org/abs/2310.16878 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Topological holography, quantum criticality, and boundary states
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local dynamics of a theory and provides a unified description of the symmetry and duality in gapped and gapless phases of matter. In this work, we develop the topological holographic picture for (1+1)d quantum phases, including both gapped phases as well as a wide…

This https://arxiv.org/abs/2505.23891 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

A microscopic Normal Matrix Model for $(A)dS_2$
We describe the duality between the gravitating $c=1$ (compact) Sine-Gordon model and a normal matrix model. From a two-dimensional quantum gravity perspective and due to the periodic nature of the potential, this model admits both anti-de Sitter and de-Sitter saddles, similarly to simpler models of Sine-Dilaton gravity, as well as more complicated interpolating "wineglass wormhole" geometries. From a string theory perspective the Euclidean de-Sitter (genus zero) saddles are related to the pres…

This https://arxiv.org/abs/2504.20227 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

On the CFT dual of superstring on AdS$_3$
In this work, we study the proposed duality between superstring on AdS$_3\times$S$^3\times\mathbb{T}^4$ with pure NS-NS flux and a deformed symmetric orbifold CFT. We extract the residues of 3-point string correlators at their next-to-leading poles, which can be expressed as integrals. Because of picture changing, the integrand is not unique. We make an ansatz for its proper form which linearly combines three different picture choices. On the CFT side, we obtain the corresponding residues by do…

This https://arxiv.org/abs/2505.23199 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Chaos in the holographic matrix models for meson and baryon
In recent years, the investigation of chaos has become a bridge connecting gravity theory and quantum field theory, especially within the framework of gauge-gravity duality. In this work, we study holographically the chaos in the matrix models for meson and baryon, which are derived from the $\mathrm{D4}/\mathrm{D6}/\overline{\mathrm{D6}}$ approach as a top-down holographic model for QCD. Since these matrix models can be simplified into coupled oscillator models with special parameters, we anal…

This https://arxiv.org/abs/2312.00871 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

The q-Schwarzian and Liouville gravity
We present a new holographic duality between q-Schwarzian quantum mechanics and Liouville gravity. The q-Schwarzian is a one parameter deformation of the Schwarzian, which is dual to JT gravity and describes the low energy sector of SYK. We show that the q-Schwarzian in turn is dual to sinh dilaton gravity. This one parameter deformation of JT gravity can be rewritten as Liouville gravity. We match the thermodynamics and classical two point function between q-Schwarzian and Liouville gravity. W…

This https://arxiv.org/abs/2505.22707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

The non-relastivistic limit of HSZ Theory
We study the non-relativistic (NR) limit of HSZ theory, a higher-derivative theory of gravity with exact and manifest T-duality invariance. Since the theory can be formulated using the generalized metric formalism, the HSZ Lagrangian remains convergent to all orders in derivatives when taking the NR limit. In this work, we analyze the three-derivative corrections to the symmetry transformations of the fields in the NR case, as well as the four-derivative action in the absence of a b-field. Inte…

Abelian dualities and line defect indices for 3d gauge theories
Hirotaka Hayashi, Tomoki Nosaka, Tadashi Okazaki
https://arxiv.org/abs/2506.01278 https://

Abelian dualities and line defect indices for 3d gauge theories
We find matching pairs of the line defect indices for 3d supersymmetric Abelian gauge theories as strong evidence of dualities of the BPS line operators. They lead to novel duality maps of the BPS line operators for $\mathcal{N}\ge 4$ supersymmetric circular and linear quiver gauge theories which can be realized as brane configurations in Type IIB string theory, including SQED, ADHM and ABJM theories.

Type II RR string fields and exotic diffeomorphisms
Raji Ashenafi Mamade, Barton Zwiebach
https://arxiv.org/abs/2506.00120 https://ar…

Type II RR string fields and exotic diffeomorphisms
We study the theory of massless fields of type II strings arising from the string field theory that uses two string fields, a physical one and an extra one that allows the writing of an action, but whose degrees of freedom ultimately decouple. The mechanism allowing the description of the self-dual five-form of type IIB, anticipated by Sen, is used by the SFT to describe all Ramond-Ramond forms in type IIB and IIA in a manifestly duality-invariant way. We find explicit expressions for the leadi…