Singular Geometry and Higgs Bundles in String Theory

TL;DR

This paper surveys recent advances in the geometric understanding of gauge fields and matter in string theory, focusing on Higgs bundles and their role in the duality framework, highlighting open problems and research directions.

Contribution

It provides an overview of current developments and open questions in the geometric engineering of physical systems using Higgs bundles in string theory.

Findings

Insights into the role of Higgs bundles in string dualities

Identification of open problems in singular geometry and Higgs bundles

Connections between brane intersections and gauge theories

Abstract

This brief survey aims to set the stage and summarize some of the ideas under discussion at the Workshop on Singular Geometry and Higgs Bundles in String Theory, to be held at the American Institute of Mathematics from October 30th to November 3rd, 2017. One of the most interesting aspects of the duality revolution in string theory is the understanding that gauge fields and matter representations can be described by intersection of branes. Since gauge theory is at the heart of our description of physical interactions, it has opened the door to the geometric engineering of many physical systems, and in particular those involving Higgs bundles. This note presents a curated overview of some current advances and open problems in the area, with no intention of being a complete review of the whole subject.