Generic matter representations in 6D supergravity theories

Abstract

In six-dimensional supergravity, there is a natural sense in which matter lying in certain representations of the gauge group is "generic," in that other "exotic" matter representations require more fine tuning. From considerations of the dimensionality of the moduli space and anomaly cancellation conditions, we find that the generic sets of matter representations are well-defined for 6D supergravity theories with gauge groups containing arbitrary numbers of nonabelian factors and U(1) factors. These generic matter representations also match with those that arise in the most generic F-theory constructions, both in 6D and in 4D, with non-generic matter representations requiring more exotic singularity types. The analysis of generic versus exotic matter illuminates long-standing puzzles regarding F-theory models with multiple U(1) factors and provides a useful framework for analyzing the 6D "swampland" of apparently consistent low-energy theories that cannot be realized through known string constructions. We note also that the matter content of the standard model is generic by the criteria used here only if the global structure is SU(3) c × SU(2) L × U(1) Y /Z 6 .

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

“…3 See, e.g. [48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76] for discussions of F-theory on elliptic fibrations with a global section. 4 When F-theory is compactified on a Calabi-Yau genus-one fibration Y , the discrete gauge group arising in this compactification is identified with the discrete part of the "Tate-Shafarevich group," X(J(Y )), of the Jacobian, J(Y ) [47,19].…”

Discrete gauge groups in certain F-theory models in six dimensions

“…This formulation enables the axiodilaton to admit an SL 2 (Z) monodromy. F-theory compactifications on elliptic fibrations with a global section have previously been analyzed [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. Furthermore, the physical interpretation of F-theory compactification on a genus-one fibration without a section was recently discussed in [30,31].…”

General F-theory models with tuned (SU(3) × SU(2) × U(1))/ℤ6 symmetry

“…In the paper [15], two of the authors of this paper described what seems to be the most generic class of tuned F-theory models that give the gauge group (SU(3) × SU(2) × U(1))/Z 6 ; these models include the CHLLT models as a particular subclass. As reviewed further in section 2.2, we focus on constructions with the group (SU(3) × SU(2) × U(1))/Z 6 , since there is a well-defined sense in which the generic matter content of models with the gauge group SU(3) × SU(2) × U(1) does not match the observed matter in the standard model [16]. A limitation of [15], however, is that the description given there of the generic (SU(3) × SU(2) × U(1))/Z 6 model was somewhat indirect.…”