A gauged baby Skyrme model and a novel BPS bound

TL;DR

This paper explores a gauged version of the baby Skyrme model, establishing a new BPS bound linked to a superpotential, and analyzes conditions for the existence of soliton solutions with these bounds.

Contribution

It introduces a novel BPS bound for the gauged baby Skyrme model and connects it to a superpotential equation, expanding understanding of soliton solutions in this context.

Findings

Existence of a BPS bound in the gauged baby Skyrme model.

The BPS bound is determined by a superpotential satisfying a specific equation.

Conditions for the existence of BPS solitons depend on the global solvability of the superpotential equation.

Abstract

The baby Skyrme model is a well-known nonlinear field theory supporting topological solitons in two space dimensions. Its action functional consists of a potential term, a kinetic term quadratic in derivatives (the "nonlinear sigma model term") and the Skyrme term quartic in first derivatives. The limiting case of vanishing sigma model term (the so-called BPS baby Skyrme model) is known to support exact soliton solutions saturating a BPS bound which exists for this model. Further, the BPS model has infinitely many symmetries and conservation laws. Recently it was found that the gauged version of the BPS baby Skyrme model with gauge group U(1) and the usual Maxwell term, too, has a BPS bound and BPS solutions saturating this bound. This BPS bound is determined by a superpotential which has to obey a superpotential equation, in close analogy to the situation in supergravity. Further, the BPS bound and the corresponding BPS solitons only may exist for potentials such that the superpotential equation has a global solution. We also briefly describe some properties of soliton solutions.