Black Hole Entropy Associated with Supersymmetric Sigma Model

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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11 pages, no figures, version to appear in the Phys. Rev. D (2003)

Scientific paper

10.1103/PhysRevD.68.104011

By means of an identity that equates elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $S^N X$ of $X$ ($S^N X=X^N/S_N$, $S_N$ is the symmetric group of $N$ elements) to the partition function of a second quantized string theory, we derive the asymptotic expansion of the partition function as well as the asymptotic for the degeneracy of spectrum in string theory. The asymptotic expansion for the state counting reproduces the logarithmic correction to the black hole entropy.

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