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

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 $S_{C{Y}_D}\sim 2\pi \sqrt{\frac{(D-3{)}^2}{2(D-1)}n}$. When D is even, we find the behavior of CY entropy behaving as $S_{C{Y}_D}\sim 2\pi \sqrt{\frac{D-1}{2}n}$. These agree with Cardy's formula at large D.

27 pages, 1 figure

Cited by in corpus (3)

• Note on Twisted Elliptic Genus of K3 Surface
• A Twisted Non-compact Elliptic Genus
• N=2 Moonshine