Thermal Correlators from Rindler-AdS$_{2}$/CFT$_{1}$

TL;DR

This paper explores the relationship between thermal two-point functions in a one-dimensional conformal field theory and their dual description in Rindler-AdS$_{2}$, revealing recurrence relations that govern their behavior.

Contribution

It demonstrates that conformal symmetry leads to recurrence relations in frequency space for thermal correlators in Rindler-AdS$_{2}$/CFT$_{1}$.

Findings

Thermal two-point functions satisfy specific recurrence relations.

Real-time correlators are solutions to these recurrence relations.

Conformal symmetry constrains the structure of thermal correlators.

Abstract

In this paper we study one-dimensional conformal field theory at finite temperature dual to the two-dimensional anti-de Sitter spacetime in the Rindler coordinates. We show that conformal symmetry for thermal two-point functions manifests itself in a form of recurrence relations in the complex frequency space. It is discussed that all the real-time two-point functions are given by solutions to the recurrence relations.