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A Simple Derivation of Finite-Temperature CFT Correlators from the BTZ Black Hole (1312.7348v2)
Published 27 Dec 2013 in hep-th, math-ph, and math.MP
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.