Toroidal and elliptic quiver BPS algebras and beyond

Toroidal and elliptic quiver BPS algebras and beyond

Blog Article

Abstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is the Handheld Games algebra underlying BPS state counting problems for toric Calabi-Yau three-folds.We introduce trigonometric and elliptic analogues of quiver Yangians, which we call toroidal quiver algebras and elliptic quiver algebras, respectively.We construct the representations of the shifted toroidal and elliptic algebras in terms of the statistical model of crystal melting.We also derive Horse Summer Sheets the algebras and their representations from equivariant localization of three-dimensional N $$ mathcal{N} $$ = 2 supersymmetric quiver gauge theories, and their dimensionally-reduced counterparts.

The analysis of supersymmetric gauge theories suggests that there exist even richer classes of algebras associated with higher-genus Riemann surfaces and generalized cohomology theories.