Duality Between the Webs of Heterotic and Type II Vacua

TL;DR

The paper investigates a duality between four-dimensional $\mathcal{N}=2$ heterotic vacua on $K3\times T^2$ and Type II vacua on Calabi–Yau manifolds, proposing a dictionary between heterotic vector bundles and Calabi–Yau geometry via reflexive polyhedra. It develops heterotic Higgsing chains and tracks resulting changes in gauge groups, tensor multiplets, and anomaly constraints, then translates these into Calabi–Yau data where $h_{11}$ and $h_{12}$ are controlled by the dual gauge content and singlets. The authors show that perturbative symmetry restoration and certain non-perturbative tensor multiplet transitions have clean polyhedral descriptions, with Dynkin diagrams readable from the polyhedra, and they find matches to known $K3$-fibered Calabi–Yau manifolds for several $k$ values. This work advances a concrete, toric-geometry–based dictionary bridging heterotic vector bundles and Calabi–Yau polyhedra, supporting the idea that many 4D $\mathcal{N}=2$ heterotic vacua possess Type II duals.

Abstract

We discuss how transitions in the space of heterotic K3*T^2 compactifications are mapped by duality into transitions in the space of Type II compactifications on Calabi-Yau manifolds. We observe that perturbative symmetry restoration, as well as non-perturbative processes such as changes in the number of tensor multiplets, have at least in many cases a simple description in terms of the reflexive polyhedra of the Calabi-Yau manifolds. Our results suggest that to many, perhaps all, four-dimensional N=2 heterotic vacua there are corresponding type II vacua.