Fivebranes and knots

2011/11/06 by Edward Witten · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Black Holes and Theoretical Physics

paper · pdf · doi:10.4171/qt/26

openalex publication_date 2011/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approaches involved other descriptions of the relevant spaces of BPS states). The starting point is a system of D3-branes ending on an NS5-brane with a nonzero theta-angle. On the one hand, this system can be related to a Chern–Simons gauge theory on the boundary of the D3-brane worldvolume; on the other hand, it can be studied by standard techniques of S-duality and T-duality. Combining the two approaches leads to a new and manifestly invariant description of the Jones polynomial of knots, and its generalizations, and to a manifestly invariant description of Khovanov homology, in terms of certain elliptic partial differential equations in four and five dimensions.

Citations

• Some Comments On String Dynamics
• On the Dynkin index of a principal \mathfraksl₂-subalgebra
• M-theory and a Topological String Duality
• SO and Sp Chern-Simons at Large N
• The Beilinson-Drinfeld Grassmannian and symplectic knot homology
• Matrix Factorizations and Kauffman Homology
• An introduction to the volume conjecture and its generalizations
• Analytic Continuation Of Chern-Simons Theory
• Recent developments in quantum key distribution: Theory and practice
• Topological insulators and superconductors
• Open BPS wall crossing and M-theory
• Twisted Whittaker model and factorizable sheaves
• State models and the jones polynomial
• A categorification of the Jones polynomial

Cited by

• M-theory [wikipedia]