Toroidal Charged AdS Branes and Deformed Toda Equations
Abstract
We show that the equations of motion for magnetically charged p-branes in (n+p+2)-dimensional AdS reduce to coupled one-dimensional Toda-type equations, and use this structure to construct static toroidal black branes with Tn symmetry and p translation-invariant directions. In the pure-Maxwell case we obtain an exact sinh solution--a (p+2)-dimensional black brane times an n-torus, asymptotically AdSp+2× Tn--whose dilatonic analogue, with a scalar coupled through eaϕ, has a running torus modulus and a non-trivial dilaton. A perturbative expansion reduces the linearized system to a pair of Pöschl-Teller equations, one elementary and one solved by associated Legendre functions of non-integer degree, so that the general solution is non-elementary; at weak coupling ε=a2 we construct the O(a2) backreaction explicitly. From the surface gravity, horizon area, and holographic renormalization we obtain the Hawking temperature, entropy density, and mass density, verifying the first law dℳ=TH ds and the traceless conformal stress tensor of the dual (p+1)-dimensional theory. At O(a2) the first law persists, but the dilaton source shifts the Stefan-Boltzmann exponent to peff=p+a2/2, breaking the clean power law s∝ THp while the normalizable dilaton hair decouples from the entropy.
Related
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BibTeX
@misc{yun2026toroidal,
title = {{Toroidal Charged AdS Branes and Deformed Toda Equations}},
author = {Sangheon Yun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23079},
eprint = {2609.23079},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23079},
}
RIS
TY - UNPB
TI - Toroidal Charged AdS Branes and Deformed Toda Equations
AU - Sangheon Yun
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.23079
UR - https://arxiv.org/abs/2609.23079
AB - We show that the equations of motion for magnetically charged p-branes in (n+p+2)-dimensional AdS reduce to coupled one-dimensional Toda-type equations, and use this structure to construct static toroidal black branes with T^n symmetry and p translation-invariant directions. In the pure-Maxwell case we obtain an exact sinh solution--a (p+2)-dimensional black brane times an n-torus, asymptotically AdS_p+2× T^n--whose dilatonic analogue, with a scalar coupled through e^aϕ, has a running torus modulus and a non-trivial dilaton. A perturbative expansion reduces the linearized system to a pair of Pöschl-Teller equations, one elementary and one solved by associated Legendre functions of non-integer degree, so that the general solution is non-elementary; at weak coupling ε=a^2 we construct the O(a^2) backreaction explicitly. From the surface gravity, horizon area, and holographic renormalization we obtain the Hawking temperature, entropy density, and mass density, verifying the first law dℳ=T_H ds and the traceless conformal stress tensor of the dual (p+1)-dimensional theory. At O(a^2) the first law persists, but the dilaton source shifts the Stefan-Boltzmann exponent to p_eff=p+a^2/2, breaking the clean power law s∝ T_H^p while the normalizable dilaton hair decouples from the entropy.
ER -