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 N=4 algebra Aκ,κ' for κ' → ∞. We also compare the answer with a counting formula derived from supergravity on AdS₃× S³ × T⁴ and find agreement within the expected range of validity.
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Maldacena et al. (1999) studied this question.