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Surface Operators and Knot Homologies

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New Trends in Mathematical Physics

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.

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Authors and Affiliations

  1. Department of Physics, University of California, Santa Barbara, CA, 93106, USA

    Sergei Gukov

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  1. Sergei Gukov
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Correspondence to Sergei Gukov .

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  1. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro, RJ, Brazil

    Vladas Sidoravičius

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Gukov, S. (2009). Surface Operators and Knot Homologies. In: Sidoravičius, V. (eds) New Trends in Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2810-5_22

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