Heterotic Gauge Structure of Type II K3 Fibrations

TL;DR

This paper explores the structure of K3 fibered Calabi-Yau manifolds, revealing their origins from orbifolds and their implications for heterotic string duals and gauge groups, including a generalization beyond hypersurfaces.

Contribution

It introduces a new construction method for Calabi-Yau threefolds with arbitrary gauge groups, extending beyond previous hypersurface limitations.

Findings

Gauge groups are determined by a single K3 surface structure.

Conifold transitions are explained via dual heterotic models.

Previous Euler number bounds are artifacts of hypersurface restrictions.

Abstract

We show that certain classes of K3 fibered Calabi-Yau manifolds derive from orbifolds of global products of K3 surfaces and particular types of curves. This observation explains why the gauge groups of the heterotic duals are determined by the structure of a single K3 surface and provides the dual heterotic picture of conifold transitions between K3 fibrations. Abstracting our construction from the special case of K3 hypersurfaces to general K3 manifolds with an appropriate automorphism, we show how to construct Calabi-Yau threefold duals for heterotic theories with arbitrary gauge groups. This generalization reveals that the previous limit on the Euler number of Calabi-Yau manifolds is an artifact of the restriction to the framework of hypersurfaces.