Refined Wall-Crossing, Free Fermions and Crystal Melting

Abstract

In this paper, we use an M-theory model to conjecture the refined reminiscence of the OSV formula connecting the refined topological string partition function with the refined BPS states partition function for the toric Calabi-Yau threefolds without any compact four cycles. Further, we show how to use the vertex operators in 2d free fermions to reproduce the refined BPS states partition function for the ${\mathbb{C}}^3$ case and the wall-crossing formulas of the refined BPS states partition function for the resolved conifold and $\mathcal{O}(-2)\oplus \mathcal{O}\to {\mathbb{P}}^1$ cases.

20 pages, 16 figues, minor corrections

References in corpus (7)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• The Refined Topological Vertex
• Crossing the Wall: Branes vs. Bundles
• Wall Crossing, Quivers and Crystals
• Computing a pyramid partition generating function with dimer shuffling
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Calabi-Yau crystals in topological string theory

Cited by in corpus (1)

• Matrix Model and Refined Wall-Crossing Formula