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Branes and Supergroups

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Abstract

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.

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  1. Department of Physics, Princeton University, Princeton, NJ, 08540, USA

    Victor Mikhaylov

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Edward Witten

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  1. Victor Mikhaylov
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Communicated by N. A. Nekrasov

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Mikhaylov, V., Witten, E. Branes and Supergroups. Commun. Math. Phys. 340, 699–832 (2015). https://doi.org/10.1007/s00220-015-2449-y

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