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 hyperKähler (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 hyperKähler manifolds, we find. When D is even, we find the behavior of CY entropy behaving as. These agree with Cardy's formula at large D.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics