Canonical Bases for Coulomb Branches

Following work of Kapustin-Saulina and Gaiotto-Moore-Neitzke it is anticipated that the expectation values of irreducible half-BPS line defects define a canonical basis in the quantized Coulomb branch of a 4d N=2 field theory. In this talk we propose a mathematical definition of the category of such defects, hence of the associated canonical basis, in the case of N=2 gauge theories of cotangent type. The definition takes the form of a finite length t-structure on the DG category of coherent sheaves on the space of triples introduced by Braverman-Finkelberg-Nakajima. This t-structure is a non-Noetherian generalization of the perverse coherent t-structure, to which it specializes in the case of pure N=2 gauge theory. It is expected that these categories categorify the cluster algebra associated to the BPS quiver of the theory, which we confirm in small examples. This is work in progress with Sabin Cautis.

Collection/Series: 
Event Type: 
Seminar
Scientific Area(s): 
Speaker(s): 
Event Date: 
Monday, September 30, 2019 - 13:30 to 15:00
Location: 
Sky Room
Room #: 
394