Recurrence Relations for Finite-Temperature Correlators via AdS${}_2$/CFT${}_1$

Abstract

This note is aimed at presenting a new algebraic approach to momentum-space correlators in conformal field theory. As an illustration we present a new Lie-algebraic method to compute frequency-space two-point functions for charged scalar operators of CFT${}_1$ dual to AdS${}_2$ black hole with constant background electric field. Our method is based on the real-time prescription of AdS/CFT correspondence, Euclideanization of AdS${}_2$ black hole and projective unitary representations of the Lie algebra $\mathfrak{sl}(2,\mathbb{R})\oplus \mathfrak{sl}(2,\mathbb{R})$. We derive novel recurrence relations for Euclidean CFT${}_1$ two-point functions, which are exactly solvable and completely determine the frequency- and charge-dependences of two-point functions. Wick-rotating back to Lorentzian signature, we obtain retarded and advanced CFT${}_1$ two-point functions that are consistent with the known results.

15 pages, 3 tikz figures; typos corrected, footnotes and references added

References in corpus (2)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Real-time response in AdS/CFT with application to spinors

Cited by in corpus (2)

• Intertwining Operator Realization of anti de Sitter Holography
• Intertwining Operator in Thermal CFT${}_d$