A note on statistical model for BPS D4-D2-D0 states

TL;DR

This paper develops a statistical model that accurately reproduces the BPS partition function for D4-D2-D0 bound states on specific toric Calabi-Yau three-folds, using combinatorial counting methods.

Contribution

It introduces a new statistical model that captures the BPS partition function for a class of Calabi-Yau three-folds with added compact cycles.

Findings

Partition function matches combinatorial counts of triangles and parallelograms.

Model applies in the small radii limit of the Calabi-Yau.

Provides a bridge between geometric configurations and statistical counting.

Abstract

We construct a statistical model that reproduces the BPS partition function of D4-D2-D0 bound states on a class of toric Calabi-Yau three-folds. The Calabi-Yau three-folds we consider are obtained by adding a compact two-cycle to $A_{N-1}$-ALE $\times \mathbb{C}$. We show that in the small radii limit of the Calabi-Yau the D4-D2-D0 partition function is correctly reproduced by counting the number of triangles and parallelograms.