Counting BPS Blackholes in Toroidal Type II String Theory

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 ${\mathcal{A}}_{\kappa ,{\kappa }^{\prime }}$ for ${\kappa }^{\prime }\to \infty$. We also compare the answer with a counting formula derived from supergravity on $Ad{S}_3\times S^3\times T^4$ and find agreement within the expected range of validity.

23 pages, harvmac. References added

References in corpus (3)

• U-duality and M-Theory
• Orbits of Exceptional Groups, Duality and BPS States in String Theory
• Riemannian Holonomy and Algebraic Geometry

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