Remarks on the interaction between Born-Infeld solitons

TL;DR

This paper investigates how replacing the gauge field action with a Born-Infeld non-linear action affects soliton solutions like vortices and monopoles in the Abelian Higgs and SU(2) models, revealing bound vortices and repulsive monopoles.

Contribution

It provides formulas to approximate the masses of Born-Infeld deformed solitons using undeformed solution data, highlighting the interaction effects in the self-dual limit.

Findings

Born-Infeld interaction causes bound vortices in the self-dual limit.

Monopoles exhibit repulsion under Born-Infeld deformation.

Approximate formulas effectively estimate soliton masses.

Abstract

We consider the Abelian Higgs model as well as the SU(2) Georgi-Glashow model in which the gauge field action is replaced by a non linear Born-Infeld action. We study soliton solutions arising in these models, namely the vortex and monopole solutions, respectively. We construct formulas which provide good approximations for the mass of the Born-Infeld deformed solitons using only the data of the undeformed solutions. The results obtained indicate that in the self-dual limit, the Born-Infeld interaction leads to bound vortices, while for monopoles it gives rise to repulsion.