Gauge Theory And Wild Ramification

TL;DR

This paper extends the gauge theory approach to the geometric Langlands program to include wild ramification, introducing new mathematical and physical tools such as irregular singularities and higher order surface operators.

Contribution

It develops a framework incorporating wild ramification into gauge theory for the geometric Langlands program, adding new elements like irregular singularities and Stokes phenomena.

Findings

Inclusion of irregular singularities in gauge theory

Introduction of higher order surface operators

Extension of the geometric Langlands correspondence

Abstract

The gauge theory approach to the geometric Langlands program is extended to the case of wild ramification. The new ingredients that are required, relative to the tamely ramified case, are differential operators with irregular singularities, Stokes phenomena, isomonodromic deformation, and, from a physical point of view, new surface operators associated with higher order singularities.