Quiver Yangian and Supersymmetric Quantum Mechanics

• DOI: 10.1007/s00220-022-04490-y
• Publication Date: 2022-09-06T07:04:30Z
• Authors: Dmitry Galakhov; Masahito Yamazaki
• Keywords: Quiver; Yangian; Instanton; Equivariant map

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.<br/>87 pages, 8 figures<br/>