nLab knot invariants via topological strings and 5-branes -- references

Knot invariants via topological strings and 5-branes

On realization of knot invariants/knot homology via topological string theory and BPS states:

• Edward Witten, Chern-Simons gauge theory as a string theory, in: The Floer memorial volume, Progr. Math. 133, Birkhäuser (1995) 637-678 [doi:10.1007/978-3-0348-9217-9, arXiv/hep-th/9207094, MR97j:57052]

• Hirosi Ooguri, Cumrun Vafa: Knot Invariants and Topological Strings, Nucl. Phys. B 577 (2000) 419-438 [doi:10.1016/S0550-3213(00)00118-8, arXiv:hep-th/9912123]

• Sergei Gukov, Albert Schwarz, Cumrun Vafa: Khovanov-Rozansky Homology and Topological Strings, Lett. Math. Phys. 74 (2005) 53-74 [doi:10.1007/s11005-005-0008-8arXiv:hep-th/0412243]

• Sergei Gukov: Surface Operators and Knot Homologies, Fortschritte der Physik 55 5-7 (2007) 473-490 [doi:10.1002/prop.200610385, arXiv:0706.2369]

• Mina Aganagic, Cumrun Vafa, Large $N$ duality, mirror symmetry, and a Q-deformed A-polynomial for knots [arXiv:1204.4709]

• Kai Wang, Shengmao Zhu: BPS invariants from framed links [arXiv:2502.16609]

Understanding this via NS5-branes/M5-branes:

• Edward Witten, Fivebranes and Knots, Quantum Topology, Volume 3, Issue 1, 2012, pp. 1-137 [arXiv:1101.3216, doi:10.4171/QT/26]

• Davide Gaiotto, Edward Witten, Knot Invariants from Four-Dimensional Gauge Theory, Advances in Theoretical and Mathematical Physics 16 3 (2012) [doi:10.4310/ATMP.2012.v16.n3.a5, arxiv:1106.4789]

• Edward Witten: Khovanov Homology And Gauge Theory, Geometry & Topology Monographs 18 (2012) 291-308 [pdf, arXiv:1108.3103]

• Sergei Gukov, Marko Stošić: Homological algebra of knots and BPS states, Geometry & Topology Monographs 18 (2012) 309-367 [doi:10.2140/gtm.2012.18.309, arXiv:1112.0030]

Review:

• Edward Witten, Khovanov Homology And Gauge Theory, Clay Conference, Oxford (October 2013) $[$pdf]

• Ross Elliot, Sergei Gukov: Section 1 of: Exceptional knot homology, Journal of Knot Theory and Its Ramifications 25 03 (2016) 1640003 [doi:10.1142/S0218216516400034, arXiv:1505.01635]

• Satoshi Nawata, Alexei Oblomkov: Lectures on knot homology, in: Physics and Mathematics of Link Homology, Contemp. Math. 680 (2016) 137 [doi:10.1090/conm/680, arXiv:1510.01795]

An alternative approach:

• Márk Mezei, Silviu S. Pufu, Yifan Wang: Chern-Simons theory from M5-branes and calibrated M2-branes, J. High Energ. Phys. 2019 165 (2019) [doi:10.1007/JHEP08(2019)165, arXiv:1812.07572]