Scalar-Vector Bootstrap

Abstract

We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.

76 pages, v3 moved several details into appendices, expanded discussion of mixed symmetry projector

References in corpus (11)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• Bootstrapping the O(N) Archipelago
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Universal anomalous dimensions at large spin and large twist
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Analytic bootstrap at large spin
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• Bounds on OPE Coefficients in 4D Conformal Field Theories

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• Conformal Collider Physics from the Lightcone Bootstrap
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• Radial expansion for spinning conformal blocks
• Seed Conformal Blocks in 4D CFT
• Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
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