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Peer-reviewedCC BYJournal of High Energy Physics

Categories of line defects and Cohomological Hall Algebras

  • Davide Gaiotto A1
  • Nikita Grygoryev1,2
  • Wei Li3
  1. 1Perimeter Institute for Theoretical Physics
  2. 2University of Waterloo
  3. 3Chinese Academy of Sciences
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Abstract

A bstract Any four-dimensional Supersymmetric Quantum Field Theory with eight super-charges 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.

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Cite

BibTeXRIS
BibTeX
@article{gaiotto2026categories,
  title = {{Categories of line defects and Cohomological Hall Algebras}},
  author = {Davide Gaiotto A and Nikita Grygoryev and Wei Li},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = jul,
  doi = {10.1007/jhep07(2026)048},
  url = {https://doi.org/10.1007/jhep07(2026)048},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Categories of line defects and Cohomological Hall Algebras
AU  - Davide Gaiotto A
AU  - Nikita Grygoryev
AU  - Wei Li
PY  - 2026
DA  - 2026/07/03
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep07(2026)048
UR  - https://doi.org/10.1007/jhep07(2026)048
AB  - A bstract Any four-dimensional Supersymmetric Quantum Field Theory with eight super-charges 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.
SN  - 1029-8479
SN  - 1126-6708
SN  - 1127-2236
ER  -