Quiver Yangian and Supersymmetric Quantum Mechanics

DOI10.1007/S00220-022-04490-YarXiv2008.07006MaRDI QIDQ6347182

Publication date: 16 August 2020

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.

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Statistical mechanics of crystals (82D25) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Phase transitions (general) in equilibrium statistical mechanics (82B26) Supersymmetry and quantum mechanics (81Q60) Fine and coarse moduli spaces (14D22) Arcs and motivic integration (14E18) Yang-Baxter equations and Rota-Baxter operators (17B38)

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