| Abstract: |
Physicists associate a hyper-Kaehler manifold, called the Coulomb branch, to a 3d N=4 supersymmetric gauge theory. (The gauge theory in question is specified by a choice of a compact Lie group G and its quaternionic representation M.) There is no mathematically understandable definition of the Coulomb branch so far, but it is expected that many interesting hyper-Kaehler manifolds, such as instanton moduli spaces, monopole moduli spaces, appear as various choices of G and M. In this talk, I will propose a mathematical definition of the Coulomb branch, as a complex algebraic variety, based on the cohomology group of certain spaces, related to affine Grassmannian. (Partly joint work with Braverman, Finkelberg) |
