Refined Wall-Crossing, Free Fermions and Crystal Melting

2010/10/02 by Haitao Liu, Jie Yang, Liu, Haitao +1
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.1010.0348

openalex publication_date 2010/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ℂ³ case and the wall-crossing formulas of the refined BPS states partition function for the resolved conifold and O(-2)\oplusO→ ℙ¹ cases.

Citations

• Crossing the Wall: Branes vs. Bundles
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
• Quantum Calabi-Yau and Classical Crystals
• Motivic degree zero Donaldson-Thomas invariants

Related

• Matrix Model and Refined Wall-Crossing Formula
• Crystals and intersecting branes
• Wall crossing in local Calabi Yau manifolds
• Consistently melting crystals
• Total partition function with fermionic number fluxes of local toric Calabi--Yau threefold and KP integrability