Charged AdS3 black branes as marginally deformed two-dimensional CFTs
Abstract
We study how boundary correlation functions encode the charge dependence of the renormalised Euclidean action of an AdS3 black brane. In three-dimensional Einstein-Maxwell theory, the Maxwell field has logarithmic asymptotics and is locally dual to a massless pseudoscalar. In the canonical ensemble, the charge density fixes the slope of a spatially linear source for the dual marginal operator. At fixed temperature, the classical action is even in the charge density due to reflection symmetry Φ→−Φ, and its charge expansion coefficients are governed by Catalan numbers. We compute the quadratic and quartic terms from connected correlation functions around the neutral brane. The scalar two-point function and the shift symmetry of its source determine the matter Weyl anomaly, which fixes the logarithmic temperature dependence of the quadratic term in the charge expansion. At quartic order, the connected four-point function comes from tree-level graviton exchange. Integrating it against the linear source, with an infrared cutoff on the overall scale of the integral, reproduces the quartic coefficient of the action per unit length. At each higher order, the corresponding Catalan coefficient predicts the integrated sum of all connected tree-level Witten diagrams.
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BibTeX
@misc{zhao2026charged,
title = {{Charged AdS$_3$ black branes as marginally deformed two-dimensional CFTs}},
author = {Suting Zhao and Gabriel Arenas-Henriquez and Yizhou Lu and Hamed Adami and René Meyer},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07019},
eprint = {2611.07019},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07019},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Charged AdS_3 black branes as marginally deformed two-dimensional CFTs
AU - Suting Zhao
AU - Gabriel Arenas-Henriquez
AU - Yizhou Lu
AU - Hamed Adami
AU - René Meyer
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07019
UR - https://arxiv.org/abs/2611.07019
AB - We study how boundary correlation functions encode the charge dependence of the renormalised Euclidean action of an AdS_3 black brane. In three-dimensional Einstein-Maxwell theory, the Maxwell field has logarithmic asymptotics and is locally dual to a massless pseudoscalar. In the canonical ensemble, the charge density fixes the slope of a spatially linear source for the dual marginal operator. At fixed temperature, the classical action is even in the charge density due to reflection symmetry Φ→−Φ, and its charge expansion coefficients are governed by Catalan numbers. We compute the quadratic and quartic terms from connected correlation functions around the neutral brane. The scalar two-point function and the shift symmetry of its source determine the matter Weyl anomaly, which fixes the logarithmic temperature dependence of the quadratic term in the charge expansion. At quartic order, the connected four-point function comes from tree-level graviton exchange. Integrating it against the linear source, with an infrared cutoff on the overall scale of the integral, reproduces the quartic coefficient of the action per unit length. At each higher order, the corresponding Catalan coefficient predicts the integrated sum of all connected tree-level Witten diagrams.
ER -