The SO(32) heterotic string on a K3 surface

The SO(32) heterotic string on a K3 surface is analyzed in terms of the dual theory of a type II string (or F-theory) on an elliptically fibred Calabi-Yau manifold. The results are in beautiful agreement with earlier work by Witten using very different methods. In particular, we find gauge groups of SO(32) × Sp(k) appearing at points in the moduli space identified with point-like instantons and see hypermultiplets in the (32, 2k) representation becoming massless at the same time. We also discuss some aspects of the E8 × E8 case.