Kavli Affiliate: Hiraku Nakajima
| Summary:
The S-dual $(mathbf G^veecurvearrowrightmathbf M^vee)$ of the pair $(mathbf Gcurvearrowrightmathbf M)$ of a smooth affine algebraic symplectic manifold $mathbf M$ with hamiltonian action of a complex reductive group $mathbf G$ was introduced implicitly in [arXiv:1706.02112] and explicitly in [arXiv:1807.09038] under the cotangent type assumption. The definition was a modification of the definition of Coulomb branches of gauge theories in [arXiv:1601.03586]. It was motivated by the S-duality of boundary conditions of 4-dimensional $mathcal N=4$ super Yang-Mills theory, studied by Gaiotto and Witten [arXiv:0807.3720]. It is also relevant to the relative Langlands duality proposed by Ben-Zvi, Sakellaridis and Venkatesh. In this article, we review the definition and properties of S-dual.
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