Quiver Yangian from Crystal Melting

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Abstract
We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau three-folds. In Type IIA superstring compactification on a toric Calabi-Yau manifold, 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 act on molten crystal configurations, hence on the BPS states contributing to the BPS degeneracy. 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.

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