Elliptic Genera of Symmetric Products and Second Quantized Strings

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 of a manifold M to the partition function of a second quantized string theory on the space . The generating function of these elliptic genera is shown to be (almost) an automorphic form for . 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.