Conformal Symmetry, Rindler Space and The AdS/CFT Correspondence

TL;DR

This paper explores how conformal symmetry emerges near black hole horizons in Rindler space within the AdS/CFT framework, revealing new insights into boundary conformal transformations and two-point functions.

Contribution

It demonstrates the role of SO(2,2) isometry conjugacy classes in generating boundary conformal transformations and provides an alternative derivation of two-point functions in Rindler space.

Findings

Conformal symmetry is enhanced near black hole horizons in Rindler space.

Loxodromy conjugacy class of SO(2,2) generates boundary conformal transformations.

Two-point functions in Rindler space can be derived via AdS/CFT correspondence.

Abstract

Field theories in black hole spacetimes undergo dimensional reduction near horizon (in the Rindler limit) to two dimensional conformal field theories. We investigate this enhancement of symmetries in the context of gauge/gravity duality by considering Rindler space as boundary of Anti-de Sitter space in three spacetime dimensions. We show that the loxodromy conjugacy class of the SO(2,2) isometry group is responsible for generating the special conformal transformations on the boundary under RG flow. We use this approach to present an alternative derivation of the two-point function in Rindler space using AdS/CFT correspondence.