Communications in Mathematical Physics

, Volume 340, Issue 2, pp 699–832 | Cite as

Branes and Supergroups

  • Victor Mikhaylov
  • Edward WittenEmail author


Extending previous work that involved D3-branes ending on a fivebrane with \({\theta_{\mathrm{YM}}\neq 0}\), we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional Chern–Simons theory of a supergroup \({{\rm U}(m|n)}\) or \({{\rm OS}_{\rm p}(m|2n)}\) rather than an ordinary Lie group as in the one-sided case. By S-duality, we deduce a dual magnetic description of the supergroup Chern–Simons theory; a slightly different duality, in the orthosymplectic case, leads to a strong-weak coupling duality between certain supergroup Chern–Simons theories on \({\mathbb{R}^{3}}\); and a further T-duality leads to a version of Khovanov homology for supergroups. Some cases of these statements are known in the literature. We analyze how these dualities act on line and surface operators.


Gauge Group Wilson Line Surface Operator Line Operator Mill Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Authors and Affiliations

  1. 1.Department of PhysicsPrinceton UniversityPrincetonUSA
  2. 2.School of Natural SciencesInstitute for Advanced StudyPrincetonUSA

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