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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• Vafa-Witten invariants from exceptional collections
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