N = 2 heterotic string threshold correction, K3 surface and generalized Kac-Moody superalgebra

We study a standard-embedding N = 2 heterotic string compactification on K3 × T2 with a Wilson line turned on and perform a world-sheet calculation of string threshold correction. The result can be expressed in terms of the quantities appearing in the two-loop calculation of bosonic string. We also comment and speculate on the relevance of our result to generalized Kac-Moody superalgebra and N = 2 heterotic-type IIA duality.