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arxiv: 1612.02479 · v2 · submitted 2016-12-07 · ✦ hep-th · math-ph· math.MP· math.SP

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Harmony of Spinning Conformal Blocks

Volker Schomerus , Evgeny Sobko , Mikhail Isachenkov
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classification ✦ hep-th math-phmath.MPmath.SP
keywords blocksconformalspinningapproachanalysisbootstrapbundlescalogero-sutherland
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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.

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    Crosscap defects from Z2 spacetime quotients in CFTs yield new crossing equations and O(N) model examples without displacement or tilt operators, forming defect conformal manifolds lacking exactly marginal operators.