Recurrence relations for finite-temperature correlators via AdS2/CFT1

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 CFT1 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 sl(2, R) circle plus sl(2, R). We derive novel recurrence relations for Euclidean CFT1 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 CFT1 two-point functions that are consistent with the known results.