Stability and Duality in N=2 Supergravity

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.