Eur. Phys. J. C (2005) 44: 607-612
https://doi.org/10.1140/epjc/s2005-02395-5

Theoretical Physics

Combinatorial identities and quantum state densitiesof supersymmetric sigma models on N-folds

¹ Instituto de Física Teórica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, São Paulo, SP, Brazil
² Departamento de Física, Universidade Estadual de Londrina, Caixa Postal 6001, Londrina-Paraná, Brazil
³ Departamento de Matemática, Universidade de Brasília, CEP: 70910-900, Brasília, DF, Brazil

^* e-mail: mabdalla@ift.unesp.br

Abstract

There is a remarkable connection between the number of quantum states of conformal theories and the sequence of dimensions of Lie algebras. In this paper, we explore this connection by computing the asymptotic expansion of the elliptic genus and the microscopic entropy of black holes associated with (supersymmetric) sigma models. The new features of these results are the appearance of correct prefactors in the state density expansion and in the coefficient of the logarithmic correction to the entropy.