Generalized gauge field theories with non-topological soliton solutions

TL;DR

This paper systematically analyzes generalized gauge field theories with non-topological soliton solutions, establishing conditions for their existence and stability, and providing methods for explicit solution determination.

Contribution

It defines the class of generalized gauge theories supporting non-topological solitons and develops methods to explicitly find and analyze their stability.

Findings

Identified conditions for soliton existence in generalized gauge theories.

Developed methods for explicit soliton solution determination.

Established criteria for linear stability of solutions.

Abstract

We perform a systematic analysis of the conditions under which \textit{generalized} gauge field theories of compact semisimple Lie groups exhibit electrostatic spherically symmetric non-topological soliton solutions in three space dimensions. By the term \textit{generalized}, we mean that the dynamics of the concerned fields is governed by lagrangian densities which are general functions of the quadratic field invariants, leading to physically consistent models. The analysis defines exhaustively the class of this kind of lagrangian models supporting those soliton solutions and leads to methods for their explicit determination. The necessary and sufficient conditions for the linear stability of the finite-energy solutions against charge-preserving perturbations are established, going beyond the usual Derrick-like criteria, which only provides necessary conditions.