F-Theory Duals of Nonperturbative Heterotic E8xE8 Vacua in Six Dimensions

TL;DR

This work provides a systematic toric-hypersurface framework to construct F-theory duals of nonperturbative heterotic vacua in six dimensions, by realizing elliptic Calabi–Yau threefolds over blow-ups of $F_n$ and mapping heterotic instanton data $(d_1,d_2)$ to the F-theory Weierstrass data under the constraint $n_T+d_1+d_2=25$. The authors use reflexive polyhedra to extract Hodge numbers and tensor multiplets, revealing a nested polyhedral structure where extra points above the $K3$ fiber track $n_T$, and they show how to realize enhanced $E_8$ via unhiggsing in this toric setting. They provide explicit constructions for $n=0$ and $n>0$ cases, analyze the corresponding polyhedra, and demonstrate consistency with heterotic anomaly cancellation and moduli counting, including the role of non-toric deformations. Overall, the paper offers an algorithmic bridge between heterotic instanton distributions and F-theory geometry, with practical implications for classifying six-dimensional dual pairs and understanding tensor multiplet dynamics.

Abstract

We present a systematic way of generating F-theory models dual to nonperturbative vacua (i.e., vacua with extra tensor multiplets) of heterotic E8xE8 strings compactified on K3, using hypersurfaces in toric varieties. In all cases, the Calabi-Yau is an elliptic fibration over a blow up of the Hirzebruch surface F_n. We find that in most cases the fan of the base of the elliptic fibration is visible in the dual polyhedron of the Calabi-Yau, and that the extra tensor multiplets are represented as points corresponding to the blow-ups of the F_n.