MS Seminar (Mathematics - String Theory)

Speaker: Harold Williams (UT Austin)
Title: The Coherent Satake Category and Line Operators in N=2 Gauge Theory
Date: Thu, Oct 20, 2016, 13:15 - 14:30
Place: Seminar Room B
Abstract: We discuss recent work showing that in type A_n the category of equivariant perverse coherent sheaves on the affine Grassmannian categorifies the cluster algebra associated to the BPS quiver of pure N=2 gauge theory. Following work of Gaiotto-Moore-Neitzke relating cluster algebras and loop operators in N=2 theories, this suggests that simple perverse coherent sheaves can be identified with Wilson-'t Hooft line operators in pure N=2 gauge theory (further expanding on a suggestion of Kapustin-Saulina). Our proofs rely on techniques developed by Kang-Kashiwara-Kim-Oh in their work on KLR algebras. We discuss a general setting of chiral tensor categories where many of the same ideas can be applied, and which abstracts formal features of irreducible line operators in 4d holomorphic-topological field theories. This is joint work with Sabin Cautis.