Super-Yang-Mills and M5-branes

TL;DR

The paper constructs a six-dimensional non-Abelian gauge framework to capture the dynamics of five-dimensional super-Yang–Mills and, by extension, aspects of M5-branes. It introduces a space-like vector $\eta^M$ whose norm sets the 5D YM coupling, builds a covariant (and later localized) 6D action, and demonstrates reduction to 5D SYM under compactification. The work obtains 1/2-BPS string and monopole solutions in the Abelian sector, analyzes KK states and instanton-induced flux quantization, and shows how Lorentz invariance and scale invariance can be restored via a local $U(1)$-like structure with a 4-form. Overall, it provides a possible avenue for a UV-like embedding of 5D SYM in 6D related to M5-brane physics, while outlining open questions about conformal symmetry and quantum consistency.

Abstract

We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge theory with the help of a space-like constant vector $η^M$, whose norm determines the Yang-Mills coupling constant. After the localization of $η^M$ the 6D gauge theory acquires Lorentzian invariance as well as scale invariance. We discuss KK states, instantons and the flux quantization. The 6D theory admits extended solutions like 1/2 BPS `strings' and monopoles.