Bounds on OPE Coefficients in 4D Conformal Field Theories

TL;DR

This paper uses numerical conformal bootstrap techniques to establish bounds on operator product expansion coefficients in four-dimensional conformal field theories, with implications for models like composite Higgs theories.

Contribution

It extends previous bootstrap bounds to tensor operators and product groups, and analyzes constraints under assumptions relevant for composite Higgs models.

Findings

Bounds on OPE coefficients of tensor operators as a function of scaling dimension.

Extended bounds to product groups SO(N)xSO(M).

Constraints on conserved current OPE coefficients with no relevant scalar operators.

Abstract

We numerically study the crossing symmetry constraints in 4D CFTs, using previously introduced algorithms based on semidefinite programming. We study bounds on OPE coefficients of tensor operators as a function of their scaling dimension and extend previous studies of bounds on OPE coefficients of conserved vector currents to the product groups SO(N)xSO(M). We also analyze the bounds on the OPE coefficients of the conserved vector currents associated with the groups SO(N), SU(N) and SO(N)xSO(M) under the assumption that in the singlet channel no scalar operator has dimension less than four, namely that the CFT has no relevant deformations. This is motivated by applications in the context of composite Higgs models, where the strongly coupled sector is assumed to be a spontaneously broken CFT with a global symmetry.