Higher Derivative Corrections to Non-Abelian Vortex Effective Theory

TL;DR

This paper develops a systematic approach to compute higher derivative corrections to the effective theories of non-Abelian vortices, enhancing understanding of soliton dynamics in gauge theories.

Contribution

It introduces a method for calculating higher derivative corrections to soliton effective theories and applies it to non-Abelian vortices, providing explicit four-derivative terms.

Findings

Derived four-derivative corrections for the vortex sigma model.

Compared corrections with Nambu-Goto and Skyrme models.

Found that instantons/monopoles inside vortices are unaffected by higher derivatives.

Abstract

We give a systematic method to calculate higher derivative corrections to low-energy effective theories of solitons, which are in general non-linear sigma models on the moduli spaces of the solitons. By applying it to the effective theory of a single BPS non-Abelian vortex in U(N) gauge theory with N fundamental Higgs fields, we obtain four derivative corrections to the effective sigma model on the moduli space C \times CP^{N-1}. We compare them with the Nambu-Goto action and the Faddeev-Skyrme model. We also show that Yang-Mills instantons/monopoles trapped inside a non-Abelian vortex membrane/string are not modified in the presence of higher derivative terms.