Holographic stress tensor correlators on higher genus Riemann surfaces

He, Song; Li , Yun-ze; Xie, Yunfei

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Holographic stress tensor correlators on higher genus Riemann surfaces

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He, Song
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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2406.04042.pdf
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Citation

He, S., Li, Y.-z., & Xie, Y. (in preparation). Holographic stress tensor correlators on higher genus Riemann surfaces.

Cite as: https://hdl.handle.net/21.11116/0000-000F-7466-C

Abstract

In this work, we present a comprehensive study of holographic stress tensor
correlators on general Riemann surfaces, extending beyond the previously
well-studied torus cases to explore higher genus conformal field theories
(CFTs) within the framework of the Anti-de Sitter/conformal field theory
(AdS/CFT) correspondence. We develop a methodological approach to compute
holographic stress tensor correlators, employing the Schottky uniformization
technique to address the handlebody solutions for higher genus Riemann
surfaces. Through rigorous calculations, we derive four-point stress tensor
correlators, alongside recurrence relations for higher-point correlators,
within the $\mathrm{AdS}_3/\mathrm{CFT}_2$ context. Additionally, our research
delves into the holography of cutoff $\mathrm{AdS}_3$ spaces, offering novel
insights into the lower-point correlators of the $T\bar{T}$-deformed theories
on higher genus Riemann surfaces up to the first deformation order.