Higgs bundle

A Higgs bundle is a mathematical structure that arises in the study of geometry and mathematical physics, particularly in the context of gauge theory and string theory. It consists of a vector bundle equipped with a differential form, called a Higgs field, that satisfies certain conditions. More specifically, a Higgs bundle can be described as follows: 1. **Vector Bundle**: You start with a vector bundle \( E \) over a complex algebraic or differentiable manifold \( X \).