A note on transition in discrete gauge groups in F-theory

Abstract

We observe a new puzzling physical phenomenon in F-theory on the multisection geometry, wherein a model without a gauge group transitions to another model with a discrete Z n gauge group via Higgsing. This phenomenon may suggest an unknown aspect of F-theory compactification on multisection geometry lacking a global section. A possible interpretation of this puzzling physical phenomenon is proposed in this note. We also propose a possible interpretation of another unnatural physical phenomenon observed for F-theory on four-section geometry, wherein a discrete Z 2 gauge group transitions to a discrete Z 4 gauge group via Higgsing as described in the previous literature. These phenomena may suggest that a (discrete) gauge group is enhanced when a multisection splits into multisections of smaller degrees, and/or it splits into a global section and a multisection of smaller degree, in the moduli of multisection geometry.

F-theory models with U(1) × ℤ2, ℤ4 and transitions in discrete gauge groups

“…There are situations in which a genus-one fibration has a global section and in which it does not have a global section; when a genus-one fibration does not have a global section, a discrete gauge group forms in F-theory on this fibration, as mentioned. Recent discussions of F-theory on genus-one fibrations without a global section can be found, for example, in [20,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45] 2 . When a genus-one fibration has a global section (in which case, the fibration is often called an elliptic fibration 3 in the F-theory literature), the U (1) gauge group forms in F-theory if the fibration has two or more independent global sections.…”

“…However, there are various other manners in which a multisection splits into multisections of smaller degrees in the moduli of multisection geometry. When studying these, physically unnatural phenomena are identified [44,45]. Under certain conditions, a four-section splits into a pair of bisections [34,44].…”

“…It was pointed out in [44] that this process appears unnatural because a discrete Z 2 gauge group appears "enhanced" to a discrete Z 4 gauge group, rather than broken down into another discrete gauge group of a smaller degree. In contrast, another puzzling physical phenomenon was observed in [45], wherein an n-section (with n ≥ 3) splits into a global section and an (n − 1)-section. This process can be viewed from the physical viewpoint as a Higgsing process wherein an F-theory model without a discrete or U (1) gauge group transitions to another model with a discrete Z n gauge group, and this also appears puzzling [45].…”

GV-Spectroscopy for F-theory on genus-one fibrations

“…admits a unique triangulation that corresponds to the three-dimensional projective space P ∆ = P 3 . The vertices correspond to the homogeneous coordinates [w : x : y : z] ∈ P 3 with 11 Geometries of this kind have also been considered in [11][12][13]. The Jacobian of nef (0,0) can be found in http://wwwth.mpp.mpg.de/members/jkeitel/weierstrass/data/0_0.txt.…”

“…This fiber has also been discussed in[7,[11][12][13] but the matter loci have not been calculated 3. F-theory compactifications on complete intersections in toric ambient spaces have also been studied from a non-fiber based perspective in[15].…”