Counting Conformal Correlators

Abstract

We introduce simple group-theoretic techniques for classifying conformally-invariant tensor-structures. With them, we classify tensor structures of general n-point functions of non-conserved operators, and $n\ge 4$-point functions of general conserved currents, with or without permutation symmetries, and in any spacetime dimension d. (The case n=3 for conserved operators will appear in subsequent work.) Our techniques are useful for bootstrap applications. The rules we derive simultaneously count tensor structures for flat-space scattering amplitudes in d+1 dimensions.

41 page

References in corpus (9)

• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Bootstrapping the O(N) Vector Models
• Spinning Conformal Blocks
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• Diagonal Limit for Conformal Blocks in d Dimensions
• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• Radial expansion for spinning conformal blocks
• On the four-point function of the stress-energy tensors in a CFT

Cited by in corpus (4)

• Operator bases, $S$-matrices, and their partition functions
• The 3d Stress-Tensor Bootstrap
• Efficient Rules for All Conformal Blocks
• Conformal Two-Point Correlation Functions from the Operator Product Expansion