Conformal correlators on the Lorentzian torus

Abstract

The general form of a 2D conformal field theory (CFT) correlator on a Euclidean Riemann surface, Lorentzian plane or Lorentzian cylinder is well known. This paper describes the general form of 2- and 3-point CFT correlators on the Lorentzian torus LT2 which arises as the conformal boundary of the group manifold SL(2,R)≃AdS3/Z. We consider only generic points, thereby omitting an analysis of contact terms, which already exhibits a surprisingly rich structure. The results are relevant to celestial holography, for which the LT2 at the boundary of Klein space is the home of the putative celestial CFT. Published by the American Physical Society 2024