### 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 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 language | English |
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Pages (from-to) | 269-297 |

Number of pages | 29 |

Journal | Letters in Mathematical Physics |

Volume | 92 |

Issue number | 3 |

DOIs | |

Publication status | Published - Apr 7 2010 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*,

*92*(3), 269-297. https://doi.org/10.1007/s11005-010-0387-3

**N = 2 Superconformal algebra and the entropy of calabi-yau manifolds.** / Eguchi, Tohru; Hikami, Kazuhiro.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 92, no. 3, pp. 269-297. https://doi.org/10.1007/s11005-010-0387-3

}

TY - JOUR

T1 - N = 2 Superconformal algebra and the entropy of calabi-yau manifolds

AU - Eguchi, Tohru

AU - Hikami, Kazuhiro

PY - 2010/4/7

Y1 - 2010/4/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77953020222&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953020222&partnerID=8YFLogxK

U2 - 10.1007/s11005-010-0387-3

DO - 10.1007/s11005-010-0387-3

M3 - Article

AN - SCOPUS:77953020222

VL - 92

SP - 269

EP - 297

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 3

ER -