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Stability and Duality in \({\mathcal{N}\,{=}\,2}\) Supergravity

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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 \({\mathcal{N}=2}\) 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 \({\mathcal{N}=(4,0)}\) CFT, which captures the degrees of freedom of a single constituent.

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  1. NHETC, Rutgers University, Piscataway, NJ, 08854-8019, USA

    Jan Manschot

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  1. Jan Manschot
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Correspondence to Jan Manschot.

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Communicated by A. Kapustin

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Manschot, J. Stability and Duality in \({\mathcal{N}\,{=}\,2}\) Supergravity. Commun. Math. Phys. 299, 651–676 (2010). https://doi.org/10.1007/s00220-010-1104-x

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