Statistical model and BPS D4-D2-D0 counting

TL;DR

This paper develops a statistical model that accurately reproduces the BPS partition function for D4-D2-D0 bound states on the resolved conifold, linking it to a combinatorial 'triangular partitions' counting problem and analyzing wall-crossing phenomena.

Contribution

It introduces a novel statistical model that captures the BPS partition function and connects it to a combinatorial counting problem, advancing understanding of wall-crossing in this context.

Findings

Partition function matches the BPS indices

Wall-crossing phenomena are characterized within the model

Triangular partitions effectively count BPS states

Abstract

We construct a statistical model that correctly reproduces the BPS partition function of D4-D2-D0 bound states on the resolved conifold. We prove that the known partition function of the BPS indices is reproduced by the counting "triangular partitions" problem. The wall-crossing phenomena in our model are also studied.