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Scalar Hair at the String-Black-Hole Correspondence
Eliseo Pavone
https://arxiv.org/abs/2608.06016 https://arxiv.org/pdf/2608.06016 https://arxiv.org/html/2608.06016
arXiv:2608.06016v1 Announce Type: new
Abstract: We study static, spherically symmetric axion--dilaton solutions of the tree-level four-dimensional string effective action. Using the sigma-model structure of the scalar sector, we show that the full family of static, spherically symmetric and asymptotically flat solutions is obtained as the $SL(2,\mathbb R)$ orbit of the pure-dilaton FJNW solution, and we characterize the associated axion--dilaton charge space. We then analyze the perturbative regime of these solutions by comparing the onset of $\alpha'$ curvature corrections with that of string-loop corrections. Finally, we apply the string--black-hole correspondence criterion to the FJNW family by evaluating the local $\alpha'$ curvature diagnostic at the physical size $R_{\rm typ}$ of a highly excited string state. With the normalization fixed on the Schwarzschild branch, Schwarzschild saturates the nominal $\alpha'$ threshold at the correspondence surface, whereas every scalar-haired FJNW branch lies above it. More generally, independently of the common overall normalization within the matching prescription, every nonzero-hair branch has a larger curvature diagnostic at the correspondence surface than Schwarzschild. Away from the correspondence point, scalar-haired exteriors may remain under $\alpha'$ control at sufficiently weak local self-gravity and may provide perturbatively controlled long-distance fields of highly excited string states whenever the local string coupling also remains weak.
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Moduli of the Sourceless Framed Beltrami-Vekua Normal Form
Daniel Alay\'on-Solarz
https://arxiv.org/abs/2608.05459 https://arxiv.org/pdf/2608.05459 https://arxiv.org/html/2608.05459
arXiv:2608.05459v1 Announce Type: new
Abstract: We study the moduli of sourceless framed Beltrami-Vekua equations under recombinations of the unknown, scalings, and orientation-preserving changes of variables. On every bounded simply connected domain, such an equation reduces to $w_{\bar z}=B\bar w$ on the unit disk, with residual symmetries given exactly by zero-free holomorphic gauges and M\"obius transformations. When $B$ is zero-free, the equation is completely classified by two data modulo M\"obius: the hyperbolic mass density $\vartheta=\tfrac14(1-|z|^2)^2|B|^2$ and the phase-curvature current $K=\Delta\arg B$, whose hyperbolic density at $C^2$ regularity is $\kappa=\Delta_{\mathrm{hyp}}\arg B$. We determine the exact range of these invariants: every positive H\"older density and every phase current arising as the Laplacian of a H\"older phase occur. For fields with zeros, the classification extends to the phase-integrable sector through the triple $(\vartheta,d\eta,d{\star}\eta)$, where $\eta=\operatorname{Im}(dB/B)$. On the tame sector, $d\eta$ is the atomic charge measure, while $d{\star}\eta$ carries the remaining phase curvature. Thus the pseudo-analytic mass and charge are numerical projections of a larger infinite-dimensional moduli space. Explicit equal-mass, equal-charge, inequivalent equations are exhibited.
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Holographic entanglement entropy with conformal boundary conditions
Elena C\'aceres, Hare Krishna, Harita Palani Balaji, Vaishnavi Patil
https://arxiv.org/abs/2608.06277 https://arxiv.org/pdf/2608.06277 https://arxiv.org/html/2608.06277
arXiv:2608.06277v1 Announce Type: new
Abstract: We study holographic entanglement entropy in 3-dimensional AdS gravity with conformal boundary conditions which fix the conformal class of the boundary metric and its extrinsic curvature, $K$, while leaving the Weyl mode dynamical. Extending Lewkowycz-Maldacena-Dong's replica construction, we derive the corresponding holographic entanglement entropy formula. We show that the fluctuating Weyl mode does not contribute additional entropy. The entropy of the full boundary is therefore the Bekenstein-Hawking entropy, and the entropy of a boundary subregion continues to obey the Ryu-Takayanagi prescription, namely, the area of a minimal surface divided by $4G_N$.
We carry out explicit calculations for global AdS, rotating and non-rotating BTZ geometries. For an interval in AdS$_3$ we find that the $K$-dependent holographic entanglement entropy is governed by $c_m=\frac{3 \ell}{2 G_N}.$ For a thermal state at high conformal temperatures we find that, the entropy is governed by $c_{\rm eff}=\frac{3 \ell}{2 G_N} \frac{K \ell- \sqrt{K^2 \ell^2-4}}{2}$, the same effective central charge that governs the Cardy-like density of states, in agreement with previous results in the literature.
Finally, we also compute the entanglement entropy directly from the conjectured dual boundary theory - a holographic CFT coupled with time-like Liouville theory and deformed by a marginal $T \bar{T}$ like operator - and find $S_{EE} =\frac{c_{\rm eff}}{3} \ln\!\left(\frac{2 R \sin\phi_0}{\epsilon}\right) .$ This result for the state with no operator insertions (vacuum state ), provides an independent boundary realization of $c_{\mathrm{eff}}$ while clarifying that this state is not the state dual to global AdS.
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Emergent gravitational action from non-local $T\bar T$-like deformations
Yun-Ze Li, Bo-Rui Li, Yu-Xiao Liu, Song He
https://arxiv.org/abs/2608.05913 https://arxiv.org/pdf/2608.05913 https://arxiv.org/html/2608.05913
arXiv:2608.05913v1 Announce Type: new
Abstract: We study the gravitational effective action induced, at first order in the deformation parameter, by non-local $T\bar T$-like deformations of quantum field theories. Using a heat-kernel formulation, we extract the local geometric terms generated by stress-tensor two-point functions, and apply the construction to free fermions, massive Maxwell theory, and second-order Yang-Mills theory. While the resulting coefficients are generally model dependent, conformal field theories contain a universal sector fixed by the central charge $C_T$. After regularization and renormalization, this sector yields finite, scheme-independent contributions organized into a finite set of curvature invariants. We further analyze trace-trace deformations, for which the relevant contact terms are determined by the Weyl anomaly, and derive the corresponding finite gravitational action for a general class of minimal non-local kernels. These results provide a quantum effective-action realization of induced gravity in which universal conformal data determine calculable contributions to the emergent geometric response.
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