N=1 Geometries via M-theory

TL;DR

This paper develops an M-theory geometric framework using a generalized Hitchin's system to describe four-dimensional N=1 gauge theories, capturing their infrared dynamics and superpotentials across various phases.

Contribution

It introduces a novel M-theory geometric setup based on a generalized Hitchin's equation for N=1 theories, extending previous methods to include superconformal, confining, and quiver gauge theories.

Findings

Spectral data encode IR properties via N=1 curves.

Superpotential determined by boundary conditions at marked points.

New results for linear and generalized quivers.

Abstract

We provide an M-theory geometric set-up to describe four-dimensional N=1 gauge theories. This is realized by a generalization of Hitchin's equation. This framework encompasses a rich class of theories including superconformal and confining ones. We show how the spectral data of the generalized Hitchin's system encode the infrared properties of the gauge theory in terms of N=1 curves. For N=1 deformations of N=2 theories in class S, we show how the superpotential is encoded in an appropriate choice of boundary conditions at the marked points in different S-duality frames. We elucidate our approach in a number of cases -- including Argyres-Douglas points, confining phases and gaugings of T_N theories -- and display new results for linear and generalized quivers.