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arXiv · 1003.1555

N=2 Superconformal Algebra and the Entropy of Calabi-Yau Manifolds

Tohru Eguchi·Kazuhiro Hikami
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Abstract

We use the representation theory of N=2 superconformal algebra to study the elliptic genera of Calabi-Yau (CY) D-folds. We compute the entropy of CY manifolds from the growth rate of multiplicities of the massive (non-BPS) representations in the decomposition of their elliptic genera. We find that the entropy of CY manifolds of complex dimension D behaves differently depending on whether D is even or odd. When D is odd, CY entropy coincides with the entropy of the corresponding hyperKahler (D-3)-folds due to a structural theorem on Jacobi forms. In particular, we find that the Calabi-Yau 3-fold has a vanishing entropy. At D>3, using our previous results on hyperKahler manifolds, we find $S_{CY_D} \sim 2π\sqrt{{(D-3)^2\over 2(D-1)}n}$. When D is even, we find the behavior of CY entropy behaving as $S_{CY_D}\sim 2 π\sqrt{{D-1\over 2}n}$. These agree with Cardy's formula at large D.

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Tohru Eguchi, Kazuhiro Hikami. 2010-03-08. N=2 Superconformal Algebra and the Entropy of Calabi-Yau Manifolds. https://doi.org/10.1007/s11005-010-0387-3

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