Classifying BPS States in Supersymmetric Gauge Theories Coupled to Higher Derivative Chiral Models

TL;DR

This paper classifies BPS states in N=1 supersymmetric gauge theories with higher derivative chiral models, revealing distinct on-shell structures and identifying various vortex, Skyrmion, and instanton solutions in different spacetime signatures.

Contribution

It introduces a classification of on-shell structures in supersymmetric gauge theories with higher derivatives and systematically identifies BPS states in both Minkowski and Euclidean spaces.

Findings

Identifies canonical and non-canonical branches with distinct BPS solutions.

Finds 1/2 BPS vortices and vortex-lumps in the canonical branch.

Finds 1/4 BPS vortices, baby Skyrmions, and instantons in specific branches.

Abstract

We study N=1 supersymmetric gauge theories coupled with higher derivative chiral models in four dimensions in the off-shell superfield formalism. We solve the equation of motion for the auxiliary fields and find two distinct on-shell structures of the Lagrangian that we call the canonical and non-canonical branches characterized by zero and non-zero auxiliary fields, respectively. We classify BPS states of the models in Minkowski and Euclidean spaces. In Minkowski space, we find Abelian and non-Abelian vortices, vortex-lumps (or gauged lumps with fractional lump charges) as 1/2 BPS states in the canonical branch and higher derivative generalization of vortices and vortex-(BPS)baby Skyrmions (or gauged BPS baby Skyrmions with fractional baby Skyrme charges) as 1/4 BPS states in the non-canonical branch. In four-dimensional Euclidean space, we find Yang-Mills instantons trapped inside a non-Abelian vortex, intersecting vortices, intersecting vortex-(BPS)baby Skyrmions as 1/4 BPS states in the canonical branch but no BPS states in the non-canonical branch other than those in the Minkowski space.