Conformal Group Theory of Tensor Structures

Understand

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.