### Abstract

In this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the N-fold symmetric product M^{N} / S_{N} of a manifold M to the partition function of a second quantized string theory on the space M × S^{1}. The generating function of these elliptic genera is shown to be (almost) an automorphic form for O(3, 2, Z). In the context of D-brane dynamics, this result gives a precise computation of the free energy of a gas of D-strings inside a higher-dimensional brane.

Original language | English (US) |
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Pages (from-to) | 197-209 |

Number of pages | 13 |

Journal | Communications In Mathematical Physics |

Volume | 185 |

Issue number | 1 |

DOIs | |

State | Published - 1997 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Dijkgraaf, R., Moore, G., Verlinde, E., & Verlinde, H. (1997). Elliptic genera of symmetric products and second quantized strings.

*Communications In Mathematical Physics*,*185*(1), 197-209. https://doi.org/10.1007/s002200050087