Instantons in Lifshitz Field Theories

TL;DR

This paper explores BPS instantons in Lifshitz-type anisotropic field theories, generalizing known instanton solutions to higher dimensions with anisotropic scaling, and maps symmetric instantons to vortices in lower-dimensional systems.

Contribution

It introduces a framework for BPS instantons in Lifshitz theories, linking instanton equations to gradient flows and applying anisotropic reductions to relate to vortex solutions.

Findings

Derived BPS instanton equations as gradient flows for superpotentials.

Mapped rotationally symmetric instantons to vortices on hyperbolic planes.

Studied specific examples including baby Skyrmions and generalized Yang-Mills instantons.

Abstract

BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kahler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4+1 dimensions, for which we take the Chern-Simons term as the superpotential.