A Study of the Higgs mechanism in Yang-Mills and Chern-Simons Field theory

Abstract

In this work, we focus on the Higgs mechanism. First, we study the symmetry breaking patterns in the fundamental and adjoint Higgs field. Next, we study the symmetry breaking patterns in the case of direct product symmetry groups with bi-fundamental matter using Singular Value Decomposition. We present here two important applications of Singular Value Decomposition to study the bi-fundamental Higgs mechanism: 1) We derive the symmetry breaking patterns for bi-fundamental SU(2)×SU(2) and SU(3)×SU(3) theories, 2) We investigate the spectrum of the difference Chern-simons theory in the presence of a generic bi-fundamental VEV, generalizing the novel Higgs mechanism in the literature.