Counting BPS Blackholes in Toroidal Type II String Theory

Details Counting BPS Blackholes in Toroidal Type II String Theory Counting BPS Blackholes in Toroidal Type II String Theory

1999-03-18

arxiv.org/abs/hep-th/9903163v2

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, harvmac. References added

Scientific paper

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 $\CN=4$ algebra $\CA_{\kappa,\kappa'}$ for $\kappa' \to \infty$. 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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