TASI Lectures on the Mathematics of String Dualities

TL;DR

This paper provides a comprehensive overview of the mathematical structures underpinning string dualities, focusing on topological string theories and their algebraic frameworks, aimed at advancing understanding in theoretical physics.

Contribution

It introduces key mathematical concepts like twisting and higher algebraic structures in the context of supersymmetric string theories and dualities, with pedagogical explanations and examples.

Findings

Clarification of topological and holomorphic twisting methods

Explanation of descent and higher algebraic structures in string theory

Review of worldsheet theories of topological strings (A- and B-models)

Abstract

In these lecture proceedings, we describe some of the fundamental mathematical concepts that underlie supersymmetric string theory and field theory, and their role in describing and testing dualities. In particular, we provide a pedagogical introduction to topological and holomorphic twisting, descent, and higher algebraic structures. Our primary examples are worldsheet theories of topological strings, namely the A- and B-models, which we briefly review. These proceedings are based on lectures given by the second author at TASI 2021.