10-12 June 2025
BITP & Zoom
Europe/Kiev timezone

1/2-BPS line defects in 4d N=2 SQFTs via Cohomological Hall algebras

11 Jun 2025, 17:20
20m
BITP & Zoom

BITP & Zoom

14b Metrolohichna str., Kyiv, Ukraine & Online
Oral talk Mathematical Physics Mathematical Physics

Speaker

Nikita Grygoryev (Perimeter Institute / University of Waterloo)

Description

Supersymmetric quantum field theories (SQFTs), particularly those with
N=2 supersymmetry in four dimensions, often exhibit intricate behaviors. Yet, their rich structures can be more tractable than those of their non-supersymmetric counterparts. Notably, their BPS sectors are governed by algebraic frameworks reminiscent of those in simpler holomorphic-topological models.

In this talk, I will focus on the 1/2-BPS line defects in such theories, which are expected to form monoidal categories endowed with additional structures, such as rigidity and a system of renormalized r-matrices. These structures encapsulate the fusion, duality and "meromorphic" brading properties of lines.

Building upon this, we propose a construction that associates to each theory a category of bimodules over the Cohomological Hall Algebra (CoHA) derived from its BPS quiver. This category is designed to mirror the anticipated properties of the category of line defects, providing a bridge between the physical intuition and mathematical formalism.

Based on joint work with Davide Gaiotto and Wei Li.

Primary author

Nikita Grygoryev (Perimeter Institute / University of Waterloo)

Co-authors

Presentation Materials

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