Thermal Correlators from Rindler-AdS${}_2$/CFT${}_1$

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.