Higgs critical exponents and conformal bootstrap in four dimensions

We investigate relevant properties of composite operators emerging in non-supersymmetric, 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, via a direct computation, that the singlet anomalous dimension is substantially larger than the adjoint one. The numerical bootstrap results are, when possible, compared to our precise findings associated to the 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 ) × SU(N ).