Stability and duality in N=2 supergravity

TL;DR

This paper investigates how wall-crossing phenomena in N=2 supergravity affect duality symmetries, analyzing BPS spectra and partition functions to confirm S-duality and electric-magnetic duality preservation, while noting the breaking of spectral flow symmetry.

Contribution

It provides a detailed analysis of BPS spectra and partition functions in N=2 supergravity, demonstrating the compatibility of wall-crossing with S-duality and electric-magnetic duality.

Findings

Partition functions are mock modular invariant, confirming S-duality.

Wall-crossing preserves electric-magnetic duality.

Wall-crossing breaks spectral flow symmetry of the N=(4,0) CFT.

Abstract

The BPS-spectrum is known to change when moduli cross a wall of marginal stability. This paper tests the compatibility of wall-crossing with S-duality and electric-magnetic duality for N=2 supergravity. To this end, the BPS-spectrum of D4-D2-D0 branes is analyzed in the large volume limit of Calabi-Yau moduli space. Partition functions are presented, which capture the stability of BPS-states corresponding to two constituents with primitive charges and supported on very ample divisors in a compact Calabi-Yau. These functions are `mock modular invariant' and therefore confirm S-duality. Furthermore, wall-crossing preserves electric-magnetic duality, but is shown to break the `spectral flow' symmetry of the N=(4,0) CFT, which captures the degrees of freedom of a single constituent.