Quiver Yangian and Supersymmetric Quantum Mechanics

TL;DR

This paper derives the quiver Yangian algebra from supersymmetric quantum mechanics on D-branes, revealing its role in crystal melting models and BPS state counting, supported by combinatorial identities and numerical checks.

Contribution

It provides a physical derivation of the quiver Yangian algebra and its action on BPS states from supersymmetric quiver quantum mechanics, connecting algebraic structures with string theory configurations.

Findings

Derivation of the quiver Yangian algebra from supersymmetric quantum mechanics.

Establishment of its action on BPS configurations in crystal melting models.

Verification of combinatorial identities through numerical computations.

Abstract

The statistical model of crystal melting represents BPS configurations of D-branes on a toric Calabi-Yau three-fold. Recently it has been noticed that an infinite-dimensional algebra, the quiver Yangian, acts consistently on the crystal-melting configurations. We physically derive the algebra and its action on the BPS states, starting with the effective supersymmetric quiver quantum mechanics on the D-brane worldvolume. This leads to remarkable combinatorial identities involving equivariant integrations on the moduli space of the quantum mechanics, which can be checked by numerical computations.