N = 2 Superconformal algebra and the entropy of calabi-yau manifolds

Tohru Eguchi, Kazuhiro Hikami

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6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)269-297
Number of pages29
JournalLetters in Mathematical Physics
Issue number3
Publication statusPublished - 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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