
TL;DR
This paper explores the relationship between brane configurations and supergroup Chern-Simons theories, revealing dualities and connections to Khovanov homology, extending previous work on D3-branes and fivebranes.
Contribution
It introduces a new duality framework linking supergroup Chern-Simons theories with brane setups and extends the understanding of their dualities and topological invariants.
Findings
Supergroup Chern-Simons theories are realized via brane configurations.
S-duality relates these theories to magnetic dual descriptions.
Connections to Khovanov homology for supergroups are established.
Abstract
Extending previous work that involved D3-branes ending on a fivebrane with , 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 U or OSp rather than an ordinary Lie group as in the one-sided case. By -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 ; and a further -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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