A geometric construction of the Witten genus, I

TL;DR

This paper presents a geometric approach to understanding the Witten genus of complex manifolds through the analysis of a specific two-dimensional quantum field theory.

Contribution

It offers a new geometric construction of the Witten genus by rigorously analyzing a related quantum field theory.

Findings

Establishes a geometric interpretation of the Witten genus.

Connects quantum field theory with complex manifold invariants.

Provides a foundation for further mathematical exploration of quantum field theoretic methods.

Abstract

I describe how the Witten genus of a complex manifold $X$ can be seen from a rigorous analysis of a certain two-dimensional quantum field theory of maps from a surface to $X$.