Higgs Critical Exponents and Conformal Bootstrap in Four Dimensions

TL;DR

This paper studies conformal fixed points in four-dimensional gauge-Yukawa theories similar to the Standard Model, analyzing operator dimensions and comparing bootstrap results with conformal field theory calculations.

Contribution

It provides new insights into the anomalous dimensions of composite operators and explicitly computes crossing symmetry relations for SU(N)×SU(N) symmetry groups.

Findings

Singlet anomalous dimension is significantly larger than the adjoint.

Bootstrap results align with conformal field theory calculations.

Explicit crossing symmetry relations for SU(N)×SU(N) are derived.

Abstract

We investigate relevant properties of composite operators emerging in nonsupersymmetric, four-dimensional gauge-Yukawa theories with interacting conformal fixed points within a precise framework. The theories investigated in this work are structurally similar to the standard model of particle interactions, but differ by developing perturbative interacting fixed points. We investigate the physical properties of the singlet and the adjoint composite operators quadratic in the Higgs field, and discover that the singlet anomalous dimension is substantially larger than the adjoint one. The numerical bootstrap results are then compared to precise four dimensional conformal field theoretical results. To accomplish this, it was necessary to calculate explicitly the crossing symmetry relations for the global symmetry group SU($N$)$\times$SU($N$).