Multicharged Dyonic Integrable Models

TL;DR

This paper introduces new integrable models with charged topological solitons related to symmetry breaking in SU(n+1) gauge theories, connecting them to a hierarchy of generalized integrable systems and analyzing their soliton solutions.

Contribution

It presents a novel class of integrable models with charged solitons, relating them to a dyonic hierarchy and exploring their solutions and symmetry properties.

Findings

Models admit U(1)⊗U(1) charged topological solitons.

Explicit relation between 1-soliton solutions of different grades.

Connection to dyonic hierarchy of generalized cKP type.

Abstract

We introduce and study new integrable models of A_n^{(1)}-Non-Abelian Toda type which admit U(1)\otimes U(1) charged topological solitons. They correspond to the symmetry breaking SU(n+1) \to SU(2)\otimes SU(2)\otimes U(1)^{n-2} and are conjectured to describe charged dyonic domain walls of N=1 SU(n+1) SUSY gauge theory in large n limit. It is shown that this family of relativistic IMs corresponds to the first negative grade q={-1} member of a dyonic hierarchy of generalized cKP type. The explicit relation between the 1-soliton solutions (and the conserved charges as well) of the IMs of grades q=-1 and q=2 is found. The properties of the IMs corresponding to more general symmetry breaking SU(n+1) \to SU(2)^{\otimes p}\otimes U(1)^{n-p} as well as IM with global SU(2) symmetries are discussed.