Derivation of Calabi-Yau Crystals from Chern-Simons Gauge Theory

TL;DR

This paper derives new crystal melting models from Chern-Simons theory that compute topological string amplitudes on the resolved conifold, revealing shifts in Kahler moduli due to non-compact D-branes and proposing their use in proving large N dualities.

Contribution

It introduces novel crystal models from Chern-Simons theory that connect to topological string amplitudes and large N dualities, including effects of D-branes on Kahler moduli.

Findings

Crystal models compute A-model amplitudes on the resolved conifold.

Kahler modulus shifts due to non-compact D-branes.

Potential use of crystal models to prove large N dualities.

Abstract

We derive new crystal melting models from Chern-Simons theory on the three-sphere. Via large N duality, these models compute amplitudes for A-model on the resolved conifold. The crystal is bounded by two walls whose distance corresponds to the Kahler modulus of the geometry. An interesting phenomenon is found where the Kahler modulus is shifted by the presence of non-compact D-branes. We also discuss the idea of using the crystal models as means of proving more general large N dualities to all order in $g_s$.