K-Theory in Quantum Field Theory
Abstract
We survey three different ways in which K-theory in all its forms enters quantum field theory. In Part 1 we give a general argument which relates topological field theory in codimension two with twisted K-theory, and we illustrate with some finite models. Part 2 is a review of pfaffians of Dirac operators, anomalies, and the relationship to differential K-theory. Part 3 is a geometric exposition of Dirac charge quantization, which in superstring theories also involves differential K-theory. Parts 2 and 3 are related by the Green-Schwarz anomaly cancellation mechanism. An appendix, joint with Jerry Jenquin, treats the partition function of Rarita-Schwinger fields.
Cite
@article{arxiv.math-ph/0206031,
title = {K-Theory in Quantum Field Theory},
author = {Daniel S. Freed},
journal= {arXiv preprint arXiv:math-ph/0206031},
year = {2007}
}
Comments
56 pages, expanded version of lectures at "Current Developments in Mathematics"