Solutions Of Four-Dimensional Field Theories Via M Theory

TL;DR

This paper develops explicit solutions for a broad class of four-dimensional N=2 supersymmetric gauge theories by leveraging brane configurations in string theory and their reinterpretation in M theory, enhancing understanding of their Coulomb branches.

Contribution

It introduces a novel approach to solving N=2 gauge theories using brane configurations in string theory and M theory, providing explicit Coulomb branch solutions.

Findings

Explicit solutions for Coulomb branches of N=2 theories

Connection between brane configurations and field theory solutions

Applicable to theories with zero or negative beta functions

Abstract

N=2 supersymmetric gauge theories in four dimensions are studied by formulating them as the quantum field theories derived from configurations of fourbranes, fivebranes, and sixbranes in Type IIA superstrings, and then reinterpreting those configurations in M theory. This approach leads to explicit solutions for the Coulomb branch of a large family of four-dimensional N=2 field theories with zero or negative beta function.