A Simple Derivation of Finite-Temperature CFT Correlators from the BTZ Black Hole

Abstract

We present a simple Lie-algebraic approach to momentum-space two-point functions of two-dimensional conformal field theory at finite temperature dual to the BTZ black hole. Making use of the real-time prescription of AdS/CFT correspondence and ladder equations of the Lie algebra $\mathfrak{so}(2,2)\cong \mathfrak{sl}(2,\mathbb{R}{)}_L\oplus \mathfrak{sl}(2,\mathbb{R}{)}_R$, we show that the finite-temperature two-point functions in momentum space satisfy linear recurrence relations with respect to the left and right momenta. These recurrence relations are exactly solvable and completely determine the momentum-dependence of retarded and advanced two-point functions of finite-temperature conformal field theory.

10 pages; typos corrected, a reference added, discussions improved

References in corpus (4)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Real-time response in AdS/CFT with application to spinors
• Helical Luttinger Liquids and Three Dimensional Black Holes

Cited by in corpus (1)

• Intertwining Operator in Thermal CFT${}_d$