Insights and Puzzles from Branes: 4d SUSY Yang-Mills from 6d Models

TL;DR

This paper explores how different 6d theories on 5-branes in M-theory relate to 4d SUSY Yang-Mills, revealing dualities between integrable structures and effective actions.

Contribution

It clarifies the connection between IIA and IIB descriptions of 5-branes and their relation to integrable systems and low-energy effective theories in 4d SUSY Yang-Mills.

Findings

IIB picture corresponds to 6d SUSY Yang-Mills theory.

IIA picture involves a SUSY self-dual 2-form theory.

IIB-IIA duality links Hitchin and Whitham integrable structures.

Abstract

5-branes of nontrivial topology are associated in the Diaconescu-Hanany-Witten-Witten (DHWW) approach with the Seiberg-Witten (SW) theory of low-energy effective actions. There are two different "pictures", related to the IIA and IIB phases of M-theory. They differ by the choice of $6d$ theory on the 5-brane world volume. In the IIB picture it is just the 6d SUSY Yang-Mills, while in the IIA picture it is a theory of SUSY self-dual 2-form. These two pictures appear capable to describe the (non-abelian) Lax operator and (abelian) low-energy effective action respectively. Thus IIB-IIA duality is related to the duality between Hitchin and Whitham integrable structures.