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Conformal group theory of tensor structures

Authors
  • Burić, Ilija1
  • Schomerus, Volker1
  • Isachenkov, Mikhail2
  • 1 DESY, Notkestraße 85, Hamburg, D-22607, Germany , Hamburg (Germany)
  • 2 IHÉS, 35 Route de Chartres, Bures-sur-Yvette, 91440, France , Bures-sur-Yvette (France)
Type
Published Article
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Publication Date
Oct 01, 2020
Volume
2020
Issue
10
Identifiers
DOI: 10.1007/JHEP10(2020)004
Source
Springer Nature
Keywords
License
Green

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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