Canonical Bases for Coulomb Branches

Abstract: Following work of Kapustin-Saulina and Gaiotto-Moore-Neitzke, one expects half-BPS line defects in a 4d N=2 field theory to form a monoidal category with a rich structure. In general, a mathematical definition of this category is not known. In this talk we discuss an algebro-geometric proposal in the case of gauge theories with polarizable matter. The proposed category is the heart of a nonstandard t-structure on the dg category of coherent sheaves on the derived Braverman-Finkelberg-Nakajima space of triples. We refer to its objects as Koszul-perverse coherent sheaves, as this t-structure interpolates between the perverse coherent t-structure and certain t-structures appearing in the theory of Koszul duality (specializing to these in the case of a pure gauge theory and an abelian gauge theory, respectively). As a byproduct, this defines a canonical basis in the associated quantized Coulomb branch by passing to classes of irreducible objects. This is joint work with Sabin Cautis.

differential geometrymetric geometry

Audience: researchers in the discipline

Western Hemisphere colloquium on geometry and physics

Series comments: Description: Biweekly colloquium of geometers and physicists

This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.