Compactifications of F-Theory on Calabi-Yau Threefolds at Constant Coupli ng

TL;DR

This paper studies special points in F-theory compactifications on elliptically fibered Calabi-Yau threefolds where the coupling is constant, revealing orbifold realizations and gauge symmetry enhancements at singularity intersections.

Contribution

It identifies conditions for constant coupling in F-theory on Calabi-Yau threefolds, including orbifold constructions and gauge symmetry enhancements at singularities.

Findings

Orbifold realizations of constant coupling points.

Gauge symmetry enhancement from intersecting singularities.

Coalescence of point-like instantons leading to Sp(k) groups.

Abstract

Generalizing the work of Sen, we analyze special points in the moduli space of the compactification of the F-theory on elliptically fibered Calabi-Yau threefolds where the coupling remains constant. These contain points where they can be realized as orbifolds of six torus $T^6$ by $Z_m \times Z_n (m, n=2, 3, 4, 6)$. At various types of intersection points of singularities, we find that the enhancement of gauge symmetries arises from the intersection of two kinds of singularities. We also argue that when we take the Hirzebruch surface as a base for the Calabi- Yau threefold, the condition for constant coupling corresponds to the case where the point like instantons coalesce, giving rise to enhanced gauge group of $Sp(k)$.