Skyrme and Faddeev models in the low-energy limit of 4d Yang-Mills-Higgs theories

Abstract

Firstly, we consider Yang-Mills theory on ${\mathbb{R}}^{3,1}$ with an adjoint Higgs field spontaneously breaking a compact gauge group $G$ to a subgroup $H$, so that the Higgs vacuum manifold forms the coset $G/H$. It is shown that in the low-energy limit, when the Higgs vacuum value is large, the 4d Yang-Mills-Higgs theory reduces to the Faddeev sigma model on ${\mathbb{R}}^{3,1}$ with $G/H$ as target. Its action contains the standard two-derivative sigma-model term as well as the four-derivative Skyrme-type term, which stabilizes solutions against scaling. Secondly, we put the Higgs field in the bi-fundamental representation of $G={\text{U}}_{+}(N)\times {\text{U}}_{-}(N)$, realizing the simplest $A_2$-type quiver gauge theory. Breaking $G$ to $H=\text{diag}(G)$, the vacuum manifold $G/H\cong \text{U}(N)$ is a group. In this case, when the Higgs vacuum value is large, the 4d $A_2$-quiver gauge theory reduces to the Skyrme sigma model on ${\mathbb{R}}^{3,1}$ with U$(N)$ as target. Thus, both the Skyrme and the Faddeev model arise as effective field theories in the infrared of Yang-Mills-Higgs models.

1+11 pages; v2: substantially rewritten with emphasis on cases of non-trivial moduli spaces of vacua

References in corpus (11)

• Skyrmion knots in frustrated magnets
• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Hopfions in chiral magnets
• Light Nuclei of Even Mass Number in the Skyrme Model
• Knots in the Skyrme-Faddeev model
• Non-Meissner electrodynamics and knotted solitons in two-component superconductors
• 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-Faddeev model from 5d super-Yang-Mills
• The Skyrme model and chiral perturbation theory

Cited by in corpus (3)

• A low-energy limit of Yang-Mills theory on de Sitter space
• Skyrme-Faddeev model from 5d super-Yang-Mills
• Dual infrared limits of 6d $\mathcal{N}$=(2,0) theory