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arXiv · 2310.15104

Conformal Correlators on the Lorentzian Torus

Walker Melton·Atul Sharma·Andrew Strominger
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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 $\mathcal{LT}^2$ 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 $\mathcal{LT}^2$ at the boundary of Klein space is the home of the putative celestial CFT.

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Walker Melton, Atul Sharma, Andrew Strominger. 2023-10-23. Conformal Correlators on the Lorentzian Torus. https://arxiv.org/abs/2310.15104

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