Skyrme model from 6d $\mathcal{N}$= (2,0) theory

Abstract

We consider 5d Yang-Mills theory with a compact ADE-type gauge group $G$ on ${\mathbb{R}}^{3,1}\times \mathcal{I}$, where $\mathcal{I}$ is an interval. The maximally supersymmetric extension of this model appears after compactification on $S^1$ of 6d $\mathcal{N}$= (2,0) superconformal field theory on ${\mathbb{R}}^{3,1}\times S_2^2$, where $S_2^2\cong \mathcal{I}\times S^1$ is a two-sphere with two punctures. In the low-energy limit, when the length of $\mathcal{I}$ becomes small, the 5d Yang-Mills theory reduces to a nonlinear sigma model on ${\mathbb{R}}^{3,1}$ with the Lie group $G$ as its target space. It contains an infinite tower of interacting fields whose leading term in the infrared is the four-derivative Skyrme term. A maximally supersymmetric generalization leading to a hyper-Kähler sigma-model target space is briefly discussed.

1+8 pages; v2: relations with effective couplings corrected

References in corpus (3)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Skyrmions, instantons and holography
• Non-Abelian sigma models from Yang-Mills theory compactified on a circle

Cited by in corpus (5)

• Super-exceptional embedding construction of the heterotic M5: Emergence of SU(2)-flavor sector
• Flux Quantization on M5-branes
• Skyrme and Faddeev models in the low-energy limit of 4d Yang-Mills-Higgs theories
• Skyrme-Faddeev model from 5d super-Yang-Mills
• Dual infrared limits of 6d $\mathcal{N}$=(2,0) theory