Perturbative sigma models, elliptic cohomology and the Witten genus
Abstract
We provide a differential cocycle model for elliptic cohomology with complex coefficients and use analytic methods to construct a cocycle representative for the Witten class in this language. Our motivation stems from the conjectural connection between 2-dimensional field theories and elliptic cohomology originally due to G. Segal and E. Witten. The specifics of our constructions are informed by the work of S. Stolz and P. Teichner on super Euclidean field theories and K. Costello's construction of the Witten genus using perturbative quantization. As a warm-up, we prove analogous results for supersymmetric quantum mechanics and K-theory with complex coefficients.
Keywords
Cite
@article{arxiv.1311.6836,
title = {Perturbative sigma models, elliptic cohomology and the Witten genus},
author = {Daniel Berwick-Evans},
journal= {arXiv preprint arXiv:1311.6836},
year = {2016}
}
Comments
Changes made from referees suggestions: statements of main theorems were sharpened, physical motivations were separated from the main mathematical discussion, and the relation to Witten's original construction was clarified