Knot invariants and M-theory: Hitchin equations, Chern-Simons actions, and surface operators



Dasgupta, Keshav, Diez, Veronica Errasti, Ramadevi, P and Tatar, Radu
(2017) Knot invariants and M-theory: Hitchin equations, Chern-Simons actions, and surface operators. PHYSICAL REVIEW D, 95 (2). 026010-.

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Abstract

Recently Witten introduced a type IIB brane construction with certain boundary conditions to study knot invariants and Khovanov homology. The essential ingredients used in his work are the topologically twisted N=4 Yang-Mills theory, localization equations and surface operators. In this paper we extend his construction in two possible ways. On one hand we show that a slight modification of Witten's brane construction could lead, using certain well-defined duality transformations, to the model used by Ooguri-Vafa to study knot invariants using gravity duals. On the other hand, we argue that both these constructions, of Witten and of Ooguri-Vafa, lead to two different seven-dimensional manifolds in M-theory from where the topological theories may appear from certain twisting of the G-flux action. The non-Abelian nature of the topological action may also be studied if we take the wrapped M2-brane states in the theory. We discuss explicit constructions of the seven-dimensional manifolds in M-theory, and show that both the localization equations and surface operators appear naturally from the Hamiltonian formalism of the theories. Knots and link invariants are then constructed using M2-brane states in both the models.

Item Type: Article
Depositing User: Symplectic Admin
Date Deposited: 23 Aug 2016 14:31
Last Modified: 16 Mar 2024 10:53
DOI: 10.1103/PhysRevD.95.026010
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3002995