Elliptic genera of symmetric products and second quantized strings

Robbert Dijkgraaf, Gregory Moore, Erik Verlinde, Herman Verlinde

Research output: Contribution to journalArticlepeer-review

298 Scopus citations


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 MN / SN of a manifold M to the partition function of a second quantized string theory on the space M × S1. 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 languageEnglish (US)
Pages (from-to)197-209
Number of pages13
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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