Lectures on the Strominger system

TL;DR

This paper introduces the Strominger system of PDEs, exploring its connections to balanced metrics, Hermite-Yang-Mills equations, and generalized geometry, with examples and recent developments in moduli theory.

Contribution

It provides an accessible overview of the Strominger system, linking it to various geometric and physical theories, and discusses recent advances in its moduli and cohomological aspects.

Findings

Connections between Strominger system and balanced metrics

Examples illustrating the system's links to physics and geometry

Recent progress in moduli space and string class theory

Abstract

These notes give an introduction to the Strominger system of partial differential equations, and are based on lectures given in September 2015 at the GEOQUANT School, held at the Institute of Mathematical Sciences (ICMAT) in Madrid. We describe the links with the theory of balanced metrics in hermitian geometry, the Hermite-Yang-Mills equations, and its origins in physics, that we illustrate with many examples. We also cover some recent developments in the moduli problem and the interrelation of the Strominger system with generalized geometry, via the cohomological notion of string class.