Dirac Families for Loop Groups as Matrix Factorizations
Algebraic Topology
2014-09-23 v1 Mathematical Physics
math.MP
Abstract
We identify the category of integrable lowest-weight representations of the loop group LG of a compact Lie group G with the linear category of twisted, conjugation-equivariant curved Fredholm complexes on the group G: namely, the twisted, equivariant matrix factorizations of a super-potential built from the loop rotation action on LG. This lifts the isomorphism of K-groups of [FHT1,2, 3] to an equivalence of categories. The construction uses families of Dirac operators.
Keywords
Cite
@article{arxiv.1409.6051,
title = {Dirac Families for Loop Groups as Matrix Factorizations},
author = {Daniel S. Freed and Constantin Teleman},
journal= {arXiv preprint arXiv:1409.6051},
year = {2014}
}
Comments
6 pages, research announcement. The complete details and background will appear in a future paper