N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds

Details N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds

2009-09-02

arxiv.org/abs/0909.0410v3

JHEP 1002:019,2010

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 1 figure

Scientific paper

10.1007/JHEP02(2010)019

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.

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