Quiver Yangian and Supersymmetric Quantum Mechanics

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.

87 pages, 8 figures

References in corpus (12)

• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• Wall-Crossing from Boltzmann Black Hole Halos
• Non-commutative Donaldson-Thomas theory and the conifold
• Crystal Melting and Toric Calabi-Yau Manifolds
• Wall crossing in local Calabi Yau manifolds
• Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions
• Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Crystal Melting and Wall Crossing Phenomena
• Exact Results in Quiver Quantum Mechanics and BPS Bound State Counting
• Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds

Cited by in corpus (33)

• Toroidal and Elliptic Quiver BPS Algebras and Beyond
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• Gauge/Bethe correspondence from quiver BPS algebras
• A Note on Quiver Quantum Toroidal Algebra
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Hunt for 3-Schur polynomials
• Quiver Yangians and Crystal Melting: A Concise Summary
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• New quiver-like varieties and Lie superalgebras
• The Origin of Calabi-Yau Crystals in BPS States Counting
• Simple Representations of BPS Algebras: the case of $Y({\widehat{\mathfrak{gl}}}_2)$
• Gauge origami and quiver W-algebras
• Crystal Melting, BPS Quivers and Plethystics
• On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry
• More on Affine Dynkin Quiver Yangians
• BPS States Meet Generalized Cohomology
• Remarks on Berry Connection in QFT, Anomalies, and Applications
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Charging solid partitions
• Wall-Crossing Effects on Quiver BPS Algebras
• Algorithms for representations of quiver Yangian algebras
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Towards the theory of Yangians
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• Supersymmetric polynomials and algebro-combinatorial duality
• An Overview of Crystals and Double Quiver Yangians
• Tunnels Under Geometries (or Instantons Know Their Algebras)
• Vogel's universality and the classification problem for Jacobi identities
• Weyl Mutations in Quiver Yangians
• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations