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

TL;DR

This paper calculates threshold corrections in a specific heterotic string compactification on K3×T2, linking the results to two-loop bosonic string calculations and exploring implications for generalized Kac-Moody superalgebras and dualities.

Contribution

It provides a detailed world-sheet calculation of string threshold corrections in N=2 heterotic compactifications with Wilson lines, connecting to algebraic structures and duality conjectures.

Findings

Threshold correction expressed via two-loop bosonic string quantities

Insights into the role of generalized Kac-Moody superalgebras

Implications for N=2 heterotic-type IIA duality

Abstract

We study a standard-embedding $N=2$ heterotic string compactification on $K3\times T^2$ 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.