Quiver BPS Algebras

Abstract: The quiver Yangian is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. In this talk I will discuss a physical construction of this algebra as it emerges from an effective quantum field theory (QFT) describing the IR physics of D-branes wrapping the three-fold. QFT setup provides as well natural trigonometric and elliptic analogues of quiver Yangians, which could be called toroidal quiver algebras and elliptic quiver algebras, respectively. The representations of the shifted rational, trigonometric and elliptic algebras can be constructed in terms of the statistical model of crystal melting. 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. If time permits, I would mention possible developments and relations to (possibly novel) integrable models. This talk is based on arXiv:2008.07006, arXiv:2106.01230, arXiv:2108.10286.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar