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The Construction of Correlators in Finite Rigid Logarithmic Conformal Field Theory
Lukas Woike
https://arxiv.org/abs/2507.22841 https://arxiv.org/pdf/2507.…

The Construction of Correlators in Finite Rigid Logarithmic Conformal Field Theory
For logarithmic conformal field theories whose monodromy data is given by a not necessarily semisimple modular category, we solve the problem of constructing and classifying the consistent systems of correlators. The correlator construction given in this article generalizes the well-known one for rational conformal field theories given by Fuchs-Runkel-Schweigert roughly twenty years ago and solves conjectures of Fuchs, Gannon, Schaumann and Schweigert. The strategy is, even in the rational spec…

Proposal for realizing Heisenberg-type quantum-spin models in Rydberg atom quantum simulators
Masaya Kunimi, Takafumi Tomita
https://arxiv.org/abs/2507.22461 https://

Proposal for realizing Heisenberg-type quantum-spin models in Rydberg atom quantum simulators
We investigate the magnetic-field dependence of the interaction between two Rydberg atoms, $|nS_{1/2}, m_J\rangle$ and $|(n+1)S_{1/2}, m_J\rangle$. In this setting, the effective spin-1/2 Hamiltonian takes the form of an {\it XXZ} model. We show that the anisotropy parameter of the {\it XXZ} model can be tuned by applying a magnetic field, and in particular, that it changes drastically near the Förster resonance points. Based on this result, we propose experimental realizations of sp…

Antimagic labelings of a complete graph
Dr A. N. Bhavale
https://arxiv.org/abs/2506.15221 https://arxiv.org/pdf/2506.15221

Antimagic labelings of a complete graph
In $1990$, Hartsfield and Ringel introduced antimagic graphs. Hartsfield and Ringel conjectured that every connected graph (and in particular, a tree) except $K_2$ is antimagic. In $2010$, Hefetz et al.\ raised two questions: Is every orientation of any simple connected undirected graph antimagic? and Given any undirected graph $G$, does there exist an orientation of $G$ which is antimagic? They call such an orientation an {\it antimagic orientation} of $G$. Recently, Bhavale provided an edge l…

Expansion of normal subsets of odd-order elements in finite groups
Chris Parker, Jack Saunders
https://arxiv.org/abs/2507.07529 https://

Expansion of normal subsets of odd-order elements in finite groups
Let $G$ be a finite group and $K$ a normal subset consisting of odd-order elements. The rational closure of $K$, denoted $\mathbf D_K$, is the set of elements $x \in G$ with the property that $\langle x \rangle = \langle y \rangle$ for some $y$ in $K$. If $K^2 \subseteq \mathbf D_K$, we prove that $\langle K \rangle$ is soluble.

On the Complexity of the Skolem Problem at Low Orders
Piotr Bacik, Jo\"el Ouaknine, James Worrell
https://arxiv.org/abs/2507.11234 https://

On the Complexity of the Skolem Problem at Low Orders
The Skolem Problem asks to determine whether a given linear recurrence sequence (LRS) $\langle u_n \rangle_{n=0}^\infty$ over the integers has a zero term, that is, whether there exists $n$ such that $u_n = 0$. Decidability of the problem is open in general, with the most notable positive result being a decision procedure for LRS of order at most 4. In this paper we consider a bounded version of the Skolem Problem, in which the input consists of an LRS $\langle u_n \rangle_{n=0}^\infty$ and a…

On the analytical approach to infinite-mode Boson-Gaussian states
Jorge R. Bola\~nos-Serv\'in, Roberto Quezada, Josu\'e I. Rios-Cangas
https://arxiv.org/abs/2506.04537

On the analytical approach to infinite-mode Boson-Gaussian states
We develop an analytical approach to quantum Gaussian states in infinite-mode representation of the Canonical Commutation Relations (CCR's), using Yosida approximations to define integrability of possibly unbounded observables with respect to a state $ρ$ ($ρ$-integrability). It turns out that all elements of the commutative $*$-algebra generated by a possibly unbounded $ρ$-integrable observable $A$, denoted by $\langle A\rangle$, are normal and $ρ\, $-integrable. Besides, $\langle A\rangle$…

The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
Mitchell Woolley
https://arxiv.org/abs/2506.08094 https://arxi…

The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
6d (2,0) SCFTs of type $\mathfrak{g}$ have protected subsectors that were conjectured in arxiv:1404.1079 to be captured by $\mathcal{W}_\mathfrak{g}$ algebras. We write down the crossing equations for mixed four-point functions $\langle S_{k_1} S_{k_2}S_{k_3}S_{k_4}\rangle$ of 1/2-BPS operators $S_{k_i}$ in 6d (2,0) theories and detail how a certain twist reduces this system to a 2d meromorphic CFT multi-correlator bootstrap problem. We identify the relevant 6d (2,0) $\mathcal{W}$-algebras of t…

Parallel spin wave for the Villain model
Paul Dario, Wei Wu
https://arxiv.org/abs/2507.04098 https://arxiv.org/pdf/2507.04098

Parallel spin wave for the Villain model
In this paper, we study the Villain model in $\mathbb{Z}^d$ in dimension $d\geq 3$. It is conjectured, that the parallel correlation function in the infinite volume Gibbs state, i.e., the map $$ x \mapsto \langle \cosθ(0) \cosθ(x) \rangle_{μ_{\mathrm{Vil}, β}} -\left( \langle \cosθ(0) \rangle_{μ_{\mathrm{Vil}, β}} \right)^2, $$ decays like $|x|^{-2(d-2)}$ as $|x| \to \infty$ at low temperature. The results of Bricmont, Fontaine, Lebowitz, Lieb, and Spencer (19…

This https://arxiv.org/abs/2409.17464 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Computation of $\langle Φ^2\rangle$ and quantum fluxes at the polar interior of a spinning black hole
Renormalization of physical quantities for quantum field theories in curved spacetimes can be achieved via the consistent subtraction of counterterms within a regularization scheme such as a point-splitting method. Pragmatic mode-sum regularization (PMR) is a point-splitting method which is particularly suitable for rotating black hole spacetimes. We extend and tailor the t-splitting variant of PMR specifically for the interior of a Kerr black hole on the axis of rotation, focusing on a minimal…