Matrix Model and Refined Wall-Crossing Formula

TL;DR

This paper develops matrix models for refined BPS state partition functions of specific Calabi-Yau geometries by inserting the identity operator into fermionic expressions, advancing the understanding of their mathematical structure.

Contribution

It introduces a method to derive matrix models for refined BPS states by inserting the identity operator into fermionic representations, providing new tools for analyzing these partition functions.

Findings

Matrix models for refined BPS states of C3, resolved conifold, and C3/Z2 constructed.

Method involves inserting the identity operator into fermionic expressions.

Enhances computational approaches for refined BPS partition functions.

Abstract

In this paper, we show how to get matrix models corresponding to the refined BPS states partition functions of $\mathbb{C}^3$, resolved conifold and $\mathbb{C}^3/\mathbb{Z}_2$ by inserting the identity operator at a proper position in the fermionic expression of the refined BPS states partition functions.