Wall Crossing and M-theory

TL;DR

This paper explores the structure of BPS bound states of D-branes on a Calabi-Yau 3-fold, revealing a connection to M-theory and topological string theory, with implications for understanding BPS spectra across moduli space.

Contribution

It demonstrates that BPS bound states form a free field Fock space and relates their generating function to the topological string partition function across all chambers.

Findings

BPS states organize into a free field Fock space.

Generating function relates to topological string partition function.

Results hold when the Calabi-Yau has no compact 4-cycles.

Abstract

We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a Calabi-Yau 3-fold X. When X has no compact 4-cyles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in M-theory compactified down to 5 dimensions by a Calabi-Yau 3-fold X. The generating function of the D-brane bound states is expressed as a reduction of the square of the topological string partition function, in all chambers of the Kahler moduli space.