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K-theoretic Coulomb branches of gauge theories

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Hiraku Nakajima
IMPU Tokyo
Thu, 2019-08-01 11:30 - 12:30
MPIM Lecture Hall

We replace equivariant homology groups by equivariant $K$-group in the mathematical definition of $3d$ $\mathcal{N}=4$ SUSY gauge theories, and define K-theoretic Coulomb branches. Gaiotto conjectures that they are Coulomb branches of $4d$ $\mathcal{N}=2$ SUSY gauge theories over $\mathbb{R}^3 \times \mathbb{S}^1$ with a generic complex structure among $\mathbb{S}^2$ of complex structures of an expected hyperk\"ahler structure. Many properties are in parallel with homology version, but we expect several new features such as cluster algebra structures.

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