Conformal Group Theory of Tensor Structures

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.
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https://hal.archives-ouvertes.fr/hal-02350109
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Submitted on : Tuesday, November 5, 2019 - 10:48:14 PM
Last modification on : Thursday, November 14, 2019 - 5:45:36 AM

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Ilija Burić, Volker Schomerus, Mikhail Isachenkov. Conformal Group Theory of Tensor Structures. 2019. ⟨hal-02350109⟩

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