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

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 $\mathcal{N}=(2,0)$ 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.

1+10 pages; v2: boundary condition corrected, 2 refs. added, matches published version

References in corpus (7)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Stationary ring solitons in field theory - knots and vortons
• Knots in the Skyrme-Faddeev model
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Non-Abelian sigma models from Yang-Mills theory compactified on a circle
• Skyrme model from 6d $\mathcal{N}$= (2,0) theory
• Skyrme and Faddeev models in the low-energy limit of 4d Yang-Mills-Higgs theories

Cited by in corpus (2)

• Skyrme and Faddeev models in the low-energy limit of 4d Yang-Mills-Higgs theories
• Dual infrared limits of 6d $\mathcal{N}$=(2,0) theory