Quiver Yangian from Crystal Melting

Abstract

We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic cycles represent the BPS states, and the fixed points of the moduli spaces of BPS states are described by statistical configurations of crystal melting. Our algebras are "bootstrapped" from the molten crystal configurations, hence they act on the BPS states. We discuss the truncation of the algebra and its relation with D4-branes. We illustrate our results in many examples, with and without compact $4$-cycles.

137 pages, 34 figures. v3: matches with JHEP version; added two footnotes on page 18 and page 114 to clarify the issue of the sign choice in the bond factors

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Cited by in corpus (46)

• Quiver Yangian and Supersymmetric Quantum Mechanics
• Shifted Quiver Yangians and Representations from BPS Crystals
• Toroidal and Elliptic Quiver BPS Algebras and Beyond
• Vafa-Witten invariants from exceptional collections
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• Gauge/Bethe correspondence from quiver BPS algebras
• A Note on Quiver Quantum Toroidal Algebra
• Quantum toroidal algebras and solvable structures in gauge/string theory
• More on topological vertex formalism for 5-brane webs with O5-plane
• R-matrix formulation of affine Yangian of $\widehat{\mathfrak{gl}}(1|1)$
• Quiver Yangians and Crystal Melting: A Concise Summary
• Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
• The Origin of Calabi-Yau Crystals in BPS States Counting
• New quiver-like varieties and Lie superalgebras
• 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
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• BPS States Meet Generalized Cohomology
• Wall-Crossing Effects on Quiver BPS Algebras
• Charging solid partitions
• On the M2-Brane Index on Noncommutative Crepant Resolutions
• Algorithms for representations of quiver Yangian algebras
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• A domain wall in twisted M-theory
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• Towards the theory of Yangians
• Supersymmetric polynomials and algebro-combinatorial duality
• Attractor invariants, brane tilings and crystals
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• An Overview of Crystals and Double Quiver Yangians
• Vogel's universality and the classification problem for Jacobi identities
• Representations of quantum toroidal superalgebras and plane $\mathbf{s}$-partitions
• Tunnels Under Geometries (or Instantons Know Their Algebras)
• 5d-4d Correspondence in Twisted M-theory on a Conifold
• Charge functions for odd dimensional partitions
• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations
• Reduced quiver quantum toroidal algebras
• Weyl Mutations in Quiver Yangians
• Free field realization of the Ding-Iohara algebra at general levels