Categories of Line Defects and Cohomological Hall Algebras
Abstract
Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a monoidal category of BPS line defects. Any Coulomb vacuum of such a theory can be conjecturally associated to an ``algebra of BPS particles'', exemplified by certain Cohomological Hall Algebras. We conjecture the existence of a monoidal functor from the category of line defects to a certain category of bimodules for the BPS Algebra in any Coulomb vacuum. We describe images of simple objects under the conjectural functor and study their monoidal structure in examples. We conjecture that the functor may be an equivalence of dg-categories and test the conjecture at the level of the equivariant Witten indices of the spaces of morphisms.
Cite
@article{arxiv.2406.07134,
title = {Categories of Line Defects and Cohomological Hall Algebras},
author = {Davide Gaiotto and Nikita Grygoryev and Wei Li},
journal= {arXiv preprint arXiv:2406.07134},
year = {2026}
}
Comments
82 pages; v2: references added, typos corrected, main conjecture reinforced with results on Schur indices and O^*-equivariance; v3: conjecture for spherical CoHAs refined