Conformal group theory of tensor structures

• Main Authors: Ilija Burić, Volker Schomerus, Mikhail Isachenkov
• Format: Article
• Language: English
• Published: SpringerOpen 2020-10-01
• Series: Journal of High Energy Physics
• Subjects: Conformal Field Theory; Global Symmetries; Space-Time Symmetries
• Online Access: http://link.springer.com/article/10.1007/JHEP10(2020)004

Abstract The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are functions of cross ratios only, and the correlation functions that depend on insertion points in the d-dimensional Euclidean space. Here we develop an entirely group theoretic approach to tensor structures, based on the Cartan decomposition of the conformal group. It provides us with a new universal formula for tensor structures and thereby a systematic derivation of crossing equations. Our approach applies to a ‘gauge’ in which the conformal blocks are wave functions of Calogero-Sutherland models rather than solutions of the more standard Casimir equations. Through this ab initio construction of tensor structures we complete the Calogero-Sutherland approach to conformal correlators, at least for four-point functions of local operators in non-supersymmetric models. An extension to defects and superconformal symmetry is possible.