The gauged BPS baby Skyrme model

TL;DR

This paper explores the gauged BPS baby Skyrme model, revealing the existence of BPS bounds and solutions, and introduces a superpotential equation crucial for understanding soliton solutions in this nonlinear field theory.

Contribution

It extends the restricted baby Skyrme model to include gauge fields, deriving a superpotential equation and analyzing conditions for BPS solutions both analytically and numerically.

Findings

Existence of a BPS bound in the gauged model.

Derivation of a superpotential equation governing solutions.

Numerical confirmation of analytical results.

Abstract

The baby Skyrme model is a well-known nonlinear field theory supporting topological solitons in two space dimensions. In the limit where the term quadratic in derivatives (the "sigma model term") vanishes some additional structure emerges. The resulting ("extreme" or "restricted" or "BPS") baby Skyrme model has exact soliton solutions saturating a BPS bound which exists for this restricted model. Further, the restricted model has infinitely many symmetries and infinitely many conservation laws. Here we consider the gauged version of the restricted baby Skyrme model with gauge group U(1) and the usual Maxwell term for the gauge field. We find that, again, there exists a BPS bound and BPS solutions saturating this bound. We further find that the whole problem is essentially determined by a new kind of superpotential equation. The BPS bound and the corresponding BPS solitons only may exist for potentials such that the superpotential equation has a solution which exists globally, i.e., on the whole target space. We also calculate soliton solutions both exactly and numerically, completely confirming our qualitative analytical results.