Skyrme-Faddeev model from 5d super-Yang-Mills

TL;DR

This paper derives a 4d Skyrme-Faddeev sigma model from a 5d super-Yang-Mills theory with ADE gauge group, showing how low-energy limits produce a nonlinear sigma model with a specific target space and higher-derivative terms.

Contribution

It demonstrates the reduction of 5d Yang-Mills-Higgs theory to a 4d sigma model with Skyrme-Faddeev term, connecting higher-dimensional gauge theories to topological soliton models.

Findings

Reduction yields a sigma model with target space G/H.

Infrared limit dominated by kinetic and Skyrme-Faddeev terms.

Provides a link between 5d super-Yang-Mills and topological solitons.

Abstract

We consider 5d Yang-Mills-Higgs theory with a compact ADE-type gauge group $G$ and one adjoint scalar field on $\mathbb{R}^{3,1}\times\mathbb{R}_+$, where $\mathbb{R}_+=[0,\infty)$ is the half-line. The maximally supersymmetric extension of this model, with five adjoint scalars, appears after a reduction of 6d ${\cal N}{=}\,(2,0)$ superconformal field theory on $\mathbb{R}^{3,1}\times\mathbb{R}_+\times S^1$ along the circle $S^1$. We show that in the low-energy limit, when momenta along $\mathbb{R}^{3,1}$ are much smaller than along $\mathbb{R}_+$, the 5d Yang-Mills-Higgs theory reduces to a nonlinear sigma model on $\mathbb{R}^{3,1}$ with a coset $G/H$ as its target space. Here $H$ is a closed subgroup of $G$ determined by the Higgs-field asymptotics at infinity. The 4d sigma model describes an infinite tower of interacting fields, and in the infrared it is dominated by the standard two-derivative kinetic term and the four-derivative Skyrme-Faddeev term.