Conformal group theory of tensor structures

A bstract 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 fun...

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Bibliographic Details
Published in:The journal of high energy physics 2020-10, Vol.2020 (10), p.1-39, Article 4
Main Authors: Burić, Ilija, Schomerus, Volker, Isachenkov, Mikhail
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Conformal Field Theory
Correlation
Correlators
Decomposition
Elementary Particles
Euclidean geometry
Euclidean space
Field theory
Global Symmetries
Group theory
High energy physics
High Energy Physics - Theory
Mathematical models
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Space-Time Symmetries
String Theory
Tensors
Wave functions
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Summary:A bstract 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.
ISSN:1029-8479
1126-6708
1029-8479
DOI:10.1007/JHEP10(2020)004