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Counting BPS Blackholes in Toroidal Type II String Theory

Juan Maldacena·Gregory Moore·Andrew Strominger
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Abstract

We derive a $U$-duality invariant formula for the degeneracies of BPS multiplets in a D1-D5 system for toroidal compactification of the type II string. The elliptic genus for this system vanishes, but it is found that BPS states can nevertheless be counted using a certain topological partition function involving two insertions of the fermion number operator. This is possible due to four extra toroidal U(1) symmetries arising from a Wigner contraction of a large $\mathcal{N}=4$ algebra $\mathcal{A}_{κ,κ'}$ for $κ' \to \infty$. We also compare the answer with a counting formula derived from supergravity on $AdS_3\times S^3 \times T^4$ and find agreement within the expected range of validity.

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Juan Maldacena, Gregory Moore, Andrew Strominger. 1999-05-14. Counting BPS Blackholes in Toroidal Type II String Theory. https://arxiv.org/abs/hep-th/9903163

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