# Coulomb branches of 3-dimensional $\mathcal N=4$ gauge theories

Presented by:
H Nakajima Kyoto University
Date:
Wednesday 29th July 2015 - 10:00 to 11:00
Venue:
INI Seminar Room 1
Abstract:
Let $M$ be a quaternionic representation of a compact Lie group $G$. Physicists study the Coulomb branch of the 3-dimensional supersymmetric gauge theory associated with $(G,M)$, which is a hyper-Kaehler manifold, but have no rigorous mathematical definition. When $M$ is of a form $N\oplus N^*$, we introduce a variant of the affine Grassmannian Steinberg variety, define convolution product on its equivariant Borel-Moore homology group, and show that it is commutative. We propose that it gives a mathematical definition of the coordinate ring of the Coulomb branch. If time permits, we will discuss examples arising from quiver gauge theories.
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