Elliptic Genera of Symmetric Products and Second Quantized Strings

Details Elliptic Genera of Symmetric Products and Second Quantized Strings Elliptic Genera of Symmetric Products and Second Quantized Strings

1996-08-15

arxiv.org/abs/hep-th/9608096v2

Commun.Math.Phys.185:197-209,1997

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, latex, 1 figure, to appear in Commun. Math. Phys

Scientific paper

10.1007/s002200050087

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 $M \times S^1$. 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.

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