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.

arXiv comment24 pages, v2: typos corrected, minor changes

References in corpus (20)

• Bounding scalar operator dimensions in 4D CFT
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Conformal Partial Waves and the Operator Product Expansion
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Precision Islands in the Ising and $O(N)$ Models
• Spinning Conformal Correlators
• Projectors, Shadows, and Conformal Blocks
• The Bootstrap Program for Boundary CFT_d
• Spinning Conformal Blocks
• Bootstrapping 3D Fermions
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• Superintegrability of $d$-dimensional Conformal Blocks
• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• Covariant Approaches to Superconformal Blocks
• Radial expansion for spinning conformal blocks
• Seed Conformal Blocks in 4D CFT
• Revisiting N=4 superconformal blocks
• Degenerate integrability of quantum spin Calogero--Moser systems
• Hamiltonian reductions of free particles under polar actions of compact Lie groups
• Derivations of the trigonometric BC(n) Sutherland model by quantum Hamiltonian reduction

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