BPS States and Vacuum Manifold of SU_q(n) Georgi-Glashow Model

TL;DR

This paper constructs a q-deformed SU(n) Georgi-Glashow model, analyzes its vacuum structure, and demonstrates the existence of monopole solutions indicated by BPS states, revealing non-commutative vacuum parameters.

Contribution

It introduces a q-deformed gauge theory with non-commutative vacuum manifold and shows monopole solutions exist within this framework.

Findings

Vacuum manifold is parameterized by non-commutative quantities

Monopole solutions exist in the q-deformed model

Presence of BPS states indicates stable monopoles

Abstract

We construct the Georgi-Glashow Lagrangian for gauge group SU_q(n). Breaking this symmetry spontaneously gives q-dependent masses of gauge field and vacuum manifold. It turned out that the vacuum manifold is parameterized by the non-commutative quantities. We showed that the monopole solutions exist in this model, which is indicated by the presence of the BPS states.