Non-Higgsable QCD and the standard model spectrum in F-theory

Abstract

Many four-dimensional supersymmetric compactifications of F-theory contain gauge groups that cannot be spontaneously broken through geometric deformations. These "non-Higgsable clusters" include realizations of SU(3), SU(2), and SU(3) × SU(2), but no SU(n) gauge groups or factors with n > 3. We study possible realizations of the standard model in F-theory that utilize non-Higgsable clusters containing SU(3) factors and show that there are three distinct possibilities. In one, fields with the non-abelian gauge charges of the standard model matter fields are localized at a single locus where non-perturbative SU(3) and SU(2) seven-branes intersect; cancellation of gauge anomalies implies that the simplest four-dimensional chiral SU(3) × SU(2) × U(1) model that may arise in this context exhibits standard model families. We identify specific geometries that realize non-Higgsable SU(3) and SU(3) × SU(2) sectors. This kind of scenario provides a natural mechanism that could explain the existence of an unbroken QCD sector, or more generally the appearance of light particles and symmetries at low energy scales.

Cost of seven-brane gauge symmetry in a quadrillion F-theory compactifications

“…Whether such enhanced symmetry loci exist, the physics that stabilizes vacua on them, and the dynamics that might drive the universe to those vacua are all relevant cosmological questions in the string landscape; see e.g. [1,2] and references therein.…”

“…These structures do not exist in eight dimensional compactifications, but do in six [8,[19][20][21][22] and four [2,[23][24][25][26] dimensional compactifications. Gauge factors that may appear on a seven-brane in such a cluster include G ∈ {E 8 , E 7 , E 6 , F 4 , SO (8), SO(7), G 2 , SU (3), SU (2)} (1) and the possible Lagrangian two-factor gauge sectors on adjacent seven-branes in such a cluster are G 1 × G 2 ∈ {SU (3) × SU (3), G 2 × SU (2), SO(7) × SU (2), SU (3) × SU (2), SU (2) × SU (2)}.…”

Tate’s algorithm for F-theory GUTs with two U(1)s

“…Our results are not restricted to F-theoretic GUT model building, and we hope that they are also useful in other areas of F-theory, for example in direct constructions of the Standard Model [51,52], in the determination of the network of resolutions of elliptic fibrations [53][54][55][56][57], or in the recent relationship drawn between elliptic fibrations with U(1)s and genus one fibrations with multisections [58][59][60].…”

Non-perturbative reheating and Nnaturalness

“…The tension with BBN arises from the need to reheat the visible sector sufficiently that its temperature is still above ∼ MeV when the inflaton's kinetic energy has redshifted enough that the universe is radiation dominated. 12 Since the maximum temperature of the visible sector is substantially larger before this time, a baryon asymmetry can still be generated by, for example, Affleck-Dine baryogenesis [58]. Our example model, with a piecewise inflaton potential and inflaton coupling with the Higgses given by eq.…”

“…Unlike low scale supersymmetry, which might be disfavoured due to its connection to moduli stabilisation in string theory [10], there is no theoretical reason to think that technicolour models would be rare. Although our present understanding of the string landscape is limited, extra gauge groups seem to be common [11][12][13] and it is known from QCD that these can break EW symmetry. 1 As a result it is interesting to explore other potential solutions to the hierarchy problem, even if the models involved require unusual or theoretically questionable features.…”