The SO(32) Heterotic String on a K3 Surface

TL;DR

This paper analyzes the SO(32) heterotic string compactified on a K3 surface using duality with type II and F-theory, confirming earlier results and exploring gauge symmetry enhancements and matter content.

Contribution

It provides a duality-based analysis of the SO(32) heterotic string on K3, matching previous findings and extending understanding of gauge groups and matter at special points in moduli space.

Findings

Gauge groups SO(32) x Sp(k) appear at specific moduli points.

Hypermultiplets in (32,2k) become massless at these points.

Results agree with earlier Witten's work using different methods.

Abstract

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) x 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 x E8 case.