Conformal correlators on the Lorentzian torus

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mi mathvariant="script">LT</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msup></a:mrow></a:math> which arises as the conformal boundary of the group manifold <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:mi>SL</d:mi><d:mo stretchy="false">(</d:mo><d:mn>2</d:mn><d:mo>,</d:mo><d:mi mathvariant="double-struck">R</d:mi><d:mo stretchy="false">)</d:mo><d:mo>≃</d:mo><d:msub><d:mrow><d:mi>AdS</d:mi></d:mrow><d:mrow><d:mn>3</d:mn></d:mrow></d:msub><d:mo>/</d:mo><d:mi mathvariant="double-struck">Z</d:mi></d:mrow></d:math>. 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 <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:msup><j:mrow><j:mi mathvariant="script">LT</j:mi></j:mrow><j:mrow><j:mn>2</j:mn></j:mrow></j:msup></j:mrow></j:math> at the boundary of Klein space is the home of the putative celestial CFT. Published by the American Physical Society 2024