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BIRS Workshop Lecture Videos

The Coulomb Branch of 3d N = 4 Gauge Theories Dimofte, Tudor


The moduli space of a 3d N = 4 gauge theory contains at least two branches, typically referred to as Higgs and Coulomb. Both are hyperkahler manifolds with some special properties, but while the Higgs branch has a straightforward classical construction, the Coulomb branch is affected by quantum corrections and has long remained mysterious. I will discuss a physically motivated construction of both the ring of holomorphic functions on the Coulomb branch and its hyperkahler structure. I also hope to touch upon boundary conditions in 3d N = 4 gauge theories, and their images on the Higgs and Coulomb branches, which tie 3d N = 4 gauge theory to geometric representation theory in mathematics. This project was initially motivated by constructions of knot homology using the 6d (2,0) theory; 3d N = 4 3 theories also arise naturally from compactification of the 6d (2,0) theory on a surface and an additional circle. (Joint work with M. Bullimore, D. Gaiotto, and J. Hilburn.)

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