Exact indices for D-particles, flow trees and the derived category

TL;DR

This paper establishes a correspondence between flow trees in supergravity and B-branes in the topological B model, refining D-particle degeneracy calculations and confirming predictions of a new elliptic genus.

Contribution

It introduces a novel method linking supergravity flow trees with B-branes, enabling refined index computations in topological string theory.

Findings

Confirmed the prediction of a new elliptic genus

Demonstrated the correspondence between flow trees and B-branes

Provided a concrete example supporting the refined computation method

Abstract

In arXiv:0909.0508 D-particle degeneracies were calculated using novel methods. By analysing this refined computation of the index in the setting of the topological B model, a correspondence is found between flow trees in the supergravity description and B-branes in the topological theory. This enables us to use the same refinement also for single flows. A concrete example will be given, providing strong support for this method, while at the same time confirming the prediction of a new elliptic genus in arXiv:0909.0508.