TY - JOUR

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

AU - Eguchi, Tohru

AU - Hikami, Kazuhiro

N1 - Funding Information:
This work is supported in part by Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010

Y1 - 2010

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.

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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 -