A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.
Quantum Calabi-Yau and Classical Crystals
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abstract
We propose a new duality involving topological strings in the limit of large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal melting, where the temperature is inverse of the string coupling constant. The crystal is a discretization of the toric base of the Calabi-Yau with lattice length $g_s$. As a strong evidence for this duality we recover the topological vertex in terms of the statistical mechanical probability distribution for crystal melting. We also propose a more general duality involving the dimer problem on periodic lattices and topological A-model string on arbitrary local toric threefolds. The $(p,q)$ 5-brane web, dual to Calabi-Yau, gets identified with the transition regions of rigid dimer configurations.
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UNVERDICTED 2representative citing papers
Construction of the scattering diagram for BPS indices on local P1 x P1 and sketch of the Split Attractor Flow Tree Conjecture for restricted central charge phase.
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Shell formulas for instantons and gauge origami
A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.
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BPS Dendroscopy on Local $\mathbb{P}^1\times \mathbb{P}^1$
Construction of the scattering diagram for BPS indices on local P1 x P1 and sketch of the Split Attractor Flow Tree Conjecture for restricted central charge phase.