Harmony of Spinning Conformal Blocks

Abstract

Conformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme. We develop a universal approach to such spinning blocks through the harmonic analysis of certain bundles over a coset of the conformal group. The resulting Casimir equations are given by a matrix version of the Calogero-Sutherland Hamiltonian that describes the scattering of interacting spinning particles in a 1-dimensional external potential. The approach is illustrated in several examples including fermionic seed blocks in 3D CFT where they take a very simple form.

24 pages, v2: typos corrected, minor changes

References in corpus (2)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Hamiltonian reductions of free particles under polar actions of compact Lie groups

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