Surface Operators and Knot Homologies
High Energy Physics - Theory
2015-05-13 v1 Geometric Topology
Quantum Algebra
Abstract
Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli space. This action plays a key role in the construction of homological knot invariants. We illustrate the general construction with examples based on surface operators in N=2 and N=4 twisted gauge theories which lead to a categorification of the Alexander polynomial, the equivariant knot signature, and certain analogs of the Casson invariant. This paper is based on a lecture delivered at the International Congress on Mathematical Physics 2006, Rio de Janeiro, and at the RTN Workshop 2006, Napoli.
Cite
@article{arxiv.0706.2369,
title = {Surface Operators and Knot Homologies},
author = {Sergei Gukov},
journal= {arXiv preprint arXiv:0706.2369},
year = {2015}
}