The elliptic genus from split flows and Donaldson-Thomas invariants

TL;DR

This paper demonstrates how to enumerate low charge D4-D2-D0 brane states on the quintic using attractor flow trees and Donaldson-Thomas invariants, incorporating instanton corrections via mirror symmetry, and supports the split flow conjecture.

Contribution

It introduces a refined index computation scheme for low charge brane systems, confirming the split flow tree conjecture and enhancing previous results.

Findings

Successful enumeration of brane states using attractor flow trees and DT invariants

Confirmation of the split flow tree conjecture in the low charge regime

Improved index computation methods for systems with larger charges

Abstract

We analyze a mixed ensemble of low charge D4-D2-D0 brane states on the quintic and show that these can be successfully enumerated using attractor flow tree techniques and Donaldson-Thomas invariants. In this low charge regime one needs to take into account worldsheet instanton corrections to the central charges, which is accomplished by making use of mirror symmetry. All the charges considered can be realized as fluxed D6-D2-D0 and anti-D6-D2-D0 pairs which we enumerate using DT invariants. Our procedure uses the low charge counterpart of the picture developed Denef and Moore. By establishing the existence of flow trees numerically and refining the index factorization scheme, we reproduce and improve some results obtained by Gaiotto, Strominger and Yin. Our results provide appealing evidence that the strong split flow tree conjecture holds and allows to compute exact results for an important sector of the theory. Our refined scheme for computing indices might shed some light on how to improve index computations for systems with larger charges.