Gauge theory and knot homologies
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 a simple example based on surface operators in 𝒩 = 4 twisted gauge theory which lead to a categorification of a variant of the Casson invariant.
- Publication:
-
Fortschritte der Physik
- Pub Date:
- May 2007
- DOI:
- 10.1002/prop.200610385
- arXiv:
- arXiv:0706.2369
- Bibcode:
- 2007ForPh..55..473G
- Keywords:
-
- High Energy Physics - Theory;
- Mathematics - Geometric Topology;
- Mathematics - Quantum Algebra
- E-Print:
- 37 pages. Based on a talk given at the ICMP 2006 and at the RTN Workshop 2006