Shifted quiver Yangians and representations from BPS crystals
Abstract
We introduce a class of new algebras, the shifted quiver Yangians, as the BPS algebras for type IIA string theory on general toric CalabiYau threefolds. We construct representations of the shifted quiver Yangian from general subcrystals of the canonical crystal. We derive our results via equivariant localization for supersymmetric quiver quantum mechanics for various framed quivers, where the framings are determined by the shape of the subcrystals.Our results unify many known BPS state counting problems, including open BPS counting, noncompact D4branes, and wall crossing phenomena, simply as different representations of the shifted quiver Yangians. Furthermore, most of our representations seem to be new, and this suggests the existence of a zoo of BPS state counting problems yet to be studied in detail.
 Publication:

Journal of High Energy Physics
 Pub Date:
 August 2021
 DOI:
 10.1007/JHEP08(2021)146
 arXiv:
 arXiv:2106.01230
 Bibcode:
 2021JHEP...08..146G
 Keywords:

 Conformal and W Symmetry;
 Quantum Groups;
 Dbranes;
 Supersymmetric Gauge Theory;
 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 81 pages, 14 figures