Black Hole Meiosis

TL;DR

This paper refines the computation of BPS bound state indices in string theory, revealing the crucial role of polar states and providing evidence for a conjectured split attractor flow tree structure, with implications for black hole microstate counting.

Contribution

It introduces a refined method for calculating BPS indices using split attractor flow trees, emphasizing the importance of polar states and their impact on elliptic genera predictions.

Findings

Refined BPS index computation method developed.

Polar states are key in determining partition functions.

Evidence supports the split attractor flow tree conjecture.

Abstract

The enumeration of BPS bound states in string theory needs refinement. Studying partition functions of particles made from D-branes wrapped on algebraic Calabi-Yau 3-folds, and classifying states using split attractor flow trees, we extend the method for computing a refined BPS index, arXiv:0810.4301. For certain D-particles, a finite number of microstates, namely polar states, exclusively realized as bound states, determine an entire partition function (elliptic genus). This underlines their crucial importance: one might call them the `chromosomes' of a D-particle or a black hole. As polar states also can be affected by our refinement, previous predictions on elliptic genera are modified. This can be metaphorically interpreted as `crossing-over in the meiosis of a D-particle'. Our results improve on hep-th/0702012, provide non-trivial evidence for a strong split attractor flow tree conjecture, and thus suggest that we indeed exhaust the BPS spectrum. In the D-brane description of a bound state, the necessity for refinement results from the fact that tachyonic strings split up constituent states into `generic' and `special' states. These are enumerated separately by topological invariants, which turn out to be partitions of Donaldson-Thomas invariants. As modular predictions provide a check on many of our results, we have compelling evidence that our computations are correct.