Surface Operators and Knot Homologies

Details Surface Operators and Knot Homologies Surface Operators and Knot Homologies

2007-06-18

arxiv.org/abs/0706.2369v1

Physics

High Energy Physics

High Energy Physics - Theory

37 pages. Based on a talk given at the ICMP 2006 and at the RTN Workshop 2006

Scientific paper

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.

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