A geometric construction of the Witten genus, I

By K. Costello. 2010

121 citations recorded by the source corpus.

I give a rigorous construction of a 2-dimensional quantum field theory of maps from an elliptic curve to a compact complex manifold X, and I show that the partition function of this theory is the Witten genus of X. The results proved here were announced (in a slightly different form) in arXiv:1006.5422.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/93eb9cdf306027ff24c9b78eae01bca5fde520e7