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Conformal Group Theory of Tensor Structures | | Ilija Buric
; Mikhail Isachenkov
; Volker Schomerus
; | | Date: |
17 Oct 2019 | | 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. | | Source: | arXiv, 1910.8099 | | Services: | Forum | Review | PDF | Favorites | |
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