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

Satoshi Ohya

doi:10.14311/ap.2014.54.0142

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arXiv · 1312.7348

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

Satoshi Ohya

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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.

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Satoshi Ohya. 2014-05-12. A Simple Derivation of Finite-Temperature CFT Correlators from the BTZ Black Hole. https://doi.org/10.14311/ap.2014.54.0142

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