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 ${\mathcal{L}\mathcal{T}}^2$ which arises as the conformal boundary of the group manifold $\mathrm{SL}(2,\mathbb{R})$ $\simeq {\text{AdS}}_3/\mathbb{Z}$. 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 ${\mathcal{L}\mathcal{T}}^2$ at the boundary of Klein space is the home of the putative celestial CFT.

12 pages