Partition functions, duality and the tube metric

Abstract

The partition function of type IIA and B strings on R 6 × K3 , in the T 4/ Z 2 orbifold limit, is explicitly computed as a modular invariant sum over spin structures required by perturbative unitarity in order to extend the analysis to include type II strings on R6 × W4 , where W4 is associated with the tube metric conformal field theory, given by the degrees of freedom transverse to the Neveu-Schwarz fivebrane solution. This generates partition functions and perturbative spectra of string theories in six space-time dimensions, associated with the modular invariants of the level- k affine SU(2) Kac-Moody algebra. These theories provide a conformal field theory (i.e. perturbative) probe of non-perturbative (fivebrane) vacua. We contrast them with theories whose N = (4, 4) sigma-model action contains n H = k + 2 hypermultiplets as well as vector supermultiplets, and where k is the level just mentioned. In Appendix B we also give a D = 6, N = (1, 1) ‘free fermion’ string model which has. a different moduli space of vacua from the 81-parameter space relevant to the above examples.