Lifshitz field theories with SDiff symmetries

TL;DR

This paper explores Lifshitz field theories with SDiff symmetries, focusing on soliton solutions like skyrmions, vortices, and monopoles, and extends the analysis to gauged versions with Chern-Simons fields.

Contribution

It introduces Lifshitz theories with SDiff symmetries that admit BPS bounds and exact soliton solutions, including time-dependent Q-balls, and studies their gauged counterparts.

Findings

Existence of BPS bound and soliton solutions in Lifshitz theories.

Construction of exact skyrmion, vortex, and monopole solutions.

Extension to gauged theories with Chern-Simons fields maintaining soliton solutions.

Abstract

We consider Lifshitz field theories with a dynamical critical exponent z equal to the dimension of space d and with a large group of base space symmetries, concretely space coordinate transformations with unit determinant ("Special Diffeomorphisms"). The field configurations of the theories considered may have the topology of skyrmions, vortices or monopoles, although we focus our detailed investigations on skyrmions. The resulting Lifshitz field theories have a BPS bound and exact soliton solutions saturating the bound, as well as time-dependent topological Q-ball solutions. Finally, we investigate the U(1) gauged versions of the Lifshitz field theories coupled to a Chern-Simons gauge field, where the BPS bound and soliton solutions saturating the bound continue to exist.