Towards effective topological gauge theories on spectral curves

TL;DR

This paper introduces a novel approach to nonperturbative quantum field theory by formulating effective gauge theories on spectral Riemann curves, providing exact solutions for certain string models and supersymmetric Yang-Mills theories.

Contribution

It proposes a new spectral curve-based framework for solving complex quantum field theories nonperturbatively, extending to various models and their generalizations.

Findings

Effective gauge theories on spectral curves can yield exact solutions.

The approach applies to 2D string models and 4D supersymmetric Yang-Mills theories.

Potential for broad generalizations to other quantum field theories.

Abstract

We discuss a general approach to the nonperturbative treatment of quantum field theories based on existence of effective gauge theory on auxiliary ''spectral" Riemann curve. We propose an effective formulation for the exact solutions to some examples of $2d$ string models and $4d$ supersymmetric Yang-Mills theories and consider their natural generalizations.