Abstract
We analyze non-Higgsable clusters of gauge groups and matter that can arise at the level of geometry in 4D F-theory models. Non-Higgsable clusters seem to be generic features of F-theory compactifications, and give rise naturally to structures that include the nonabelian part of the standard model gauge group and certain specific types of potential dark matter candidates. In particular, there are nine distinct single nonabelian gauge group factors, and only five distinct products of two nonabelian gauge group factors with matter, including $SU(3) \times SU(2)$, that can be realized through 4D non-Higgsable clusters. There are also more complicated configurations involving more than two gauge factors; in particular, the collection of gauge group factors with jointly charged matter can exhibit branchings, loops, and long linear chains.
Highlights
SU(3), SO(8), or E8 under which there are no charged matter fields
In [4], we performed a systematic analysis of the possible non-Higgsable structures that can arise in 6D F-theory compactifications, and identified all possible “nonHiggsable clusters” of gauge group factors connected by jointly charged matter that cannot be broken by Higgsing
We have initiated a systematic analysis of geometric non-Higgsable clusters that can arise in threefolds B3 for F-theory compactifications that give N = 1 supergravity theories in four dimensions
Summary
We summarize a few of the basic features of F-theory that are central to the analysis of this paper. A supersymmetric F-theory compactification to 10 − 2n dimensions is defined by a complex n-fold base Bn that supports an elliptic fibration with section π : X → Bn where the total space X is a Calabi-Yau (n+1)-fold. The data of such an elliptic fibration can be described by a Weierstrass model [30]. For the purposes of this paper, the most relevant fact is that, in general, matter arises at codimension two loci within codimension one divisors carrying gauge group factors, where the degrees of vanishing of f , g, and/or ∆ are enhanced. While it is possible that there is some problem or inconsistency in models with such codimension three singularities, it is plausible that such models represent perfectly acceptable F-theory vacua. We do not try to resolve this question in this paper, but we do note some circumstances when this issue may affect some of the structures we describe for 4D non-Higgsable clusters
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
