N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds

Abstract

We study the elliptic genera of hyperKahler manifolds using the representation theory of N=4 superconformal algebra. We consider the decomposition of the elliptic genera in terms of N=4 irreducible characters, and derive the rate of increase of the multiplicities of half-BPS representations making use of Rademacher expansion. Exponential increase of the multiplicity suggests that we can associate the notion of an entropy to the geometry of hyperKahler manifolds. In the case of symmetric products of K3 surfaces our entropy agrees with the black hole entropy of D5-D1 system.

25 pages, 1 figure

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• Mock (False) Theta Functions as Quantum Invariants
• On the Quantum Invariant for the Spherical Seifert Manifold
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• N=2 Superconformal Algebra and the Entropy of Calabi-Yau Manifolds
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• Twisted elliptic genus for K3 and Borcherds product
• On Mathieu moonshine and Gromov-Witten invariants
• Calabi-Yau manifolds and sporadic groups