A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions

TL;DR

This paper constructs a 6D non-Abelian gauge theory for chiral 2-forms that reduces to Yang-Mills in 5D and circumvents previous no-go theorems through nonlocality along a compact dimension.

Contribution

It introduces a non-Abelian self-dual gauge theory in 6D with a compact dimension, overcoming prior theoretical limitations.

Findings

Reduces to 5D Yang-Mills at small radius R

Equivalent to Abelian chiral 2-forms in the Abelian limit

Circumvents no-go theorems via nonlocality along the compact dimension

Abstract

We construct a non-Abelian gauge theory of chiral 2-forms (self-dual gauge fields) in 6 dimensions with a spatial direction compactified on a circle of radius R. It has the following two properties. (1) It reduces to the Yang-Mills theory in 5 dimensions for small R. (2) It is equivalent to the Lorentz-invariant theory of Abelian chiral 2-forms when the gauge group is Abelian. Previous no-go theorems prohibiting non-Abelian deformations of the chiral 2-form gauge theory are circumvented by introducing nonlocality along the compactified dimension.