Mass Degeneracies In Self-Dual Models

TL;DR

This paper explores the mass spectra and vacuum structures of self-dual Chern-Simons-Higgs models, revealing their algebraic origins, supersymmetric relations, and connections to Toda equations.

Contribution

It introduces an algebraic restriction leading to coupled abelian models with specific mass spectra and links the self-duality equations to deformed Toda equations.

Findings

Mass spectra relate to gauge algebra exponents

Vacua characterized by SU(2) embeddings

Masses coincide in broken phases

Abstract

An algebraic restriction of the nonabelian self-dual Chern-Simons-Higgs systems leads to coupled abelian models with interesting mass spectra. The vacua are characterized by embeddings of $SU(2)$ into the gauge algebra, and in the broken phases the gauge and real scalar masses coincide, reflecting the relation of these self-dual models to $N=2$ SUSY. The masses themselves are related to the exponents of the gauge algebra, and the self-duality equation is a deformation of the classical Toda equations.