F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds

TL;DR

This work constructs globally consistent $D3$-tadpole cancelling $SU(5)$ F-theory GUT vacua on compact elliptically fibered Calabi-Yau fourfolds built as complete intersections in toric ambient spaces. It combines toric techniques with a split spectral-cover description of gauge flux to realize chiral matter on GUT divisors provided by non-generic del Pezzo surfaces, while implementing hypercharge flux to break $SU(5)$ to the Standard Model. A physically viable decoupling limit is demonstrated: the GUT brane can contract to a curve while the bulk volume $\mathrm{Vol}(B)$ grows, enabling gravity to decouple from the GUT sector without leaving the supergravity regime. The paper provides an explicit three-generation example on a $P^4[3]$-based fourfold, showing that the Euler characteristic suffices for tadpole cancellation and that a consistent $D$-term SUSY condition can be met within the Kähler cone, with $n_{\rm D3}=80$ in the explicit case.

Abstract

We present compact three-generation F-theory GUT models meeting in particular the constraints of D3-tadpole cancellation and D-term supersymmetry. To this end we explicitly construct elliptically fibered Calabi-Yau fourfolds as complete intersections in a toric ambient space. Toric methods enable us to control the singular geometry of the SU(5) GUT model. The GUT brane wraps a non-generic del Pezzo surface admitting GUT symmetry breaking via hypercharge flux. It is contractible to a curve and we demonstrate the existence of a consistent decoupling limit. We compute the Euler characteristic of the singular Calabi-Yau fourfold to show that our three-generation flux solutions obtained via the spectral cover construction are consistent with D3-tadpole cancellation.