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Abstract We parametrise the space of all possible flavour non-universal u $$ \mathfrak{u} $$ (1) X extensions of the Standard Model that embed inside anomaly-free semi-simple gauge theories, including up to three right-handed neutrinos. More generally, we parametrise all abelian extensions (i.e. by any number of u $$ \mathfrak{u} $$ (1)’s) of the SM with such semi-simple completions. The resulting space of abelian extensions is a collection of planes of dimensions ≤ 6. Numerically, we find that roughly 2.5% of anomaly-free u $$ \mathfrak{u} $$ (1) X extensions of the SM with a maximum charge ratio of ±10 can be embedded in such semi-simple gauge theories. Any vector-like anomaly-free abelian extension embeds (at least) inside g $$ \mathfrak{g} $$ = su $$ \mathfrak{su} $$ (12) ⊕ su $$ \mathfrak{su} $$ (2) L ⊕ su $$ \mathfrak{su} $$ (2) R . We also provide a simple computer program that tests whether a given u 1 X 1 $$ \mathfrak{u}{(1)}_{X^1} $$ ⊕ u 1 X 2 $$ \mathfrak{u}{(1)}_{X^2} $$ ⊕ . . . charge assignment has a semi-simple completion and, if it does, outputs a set of maximal gauge algebras in which the sm $$ \mathfrak{sm} $$ ⊕ u 1 X 1 $$ \mathfrak{u}{(1)}_{X^1} $$ ⊕ u 1 X 2 $$ \mathfrak{u}{(1)}_{X^2} $$ ⊕ . . . model may be embedded. We hope this is a useful tool in pointing the way from sm $$ \mathfrak{sm} $$ ⊕ u 1 X 1 $$ \mathfrak{u}{(1)}_{X^1} $$ ⊕ u 1 X 2 $$ \mathfrak{u}{(1)}_{X^2} $$ ⊕ . . . models, which have many phenomenological uses, to their unified gauge completions in the ultraviolet.

Abstract We propose that the electroweak and flavour quantum numbers of the Standard Model (SM) could be unified at high energies in an SU(4) × Sp(6) L × Sp(6) R anomaly-free gauge model. All the SM fermions are packaged into two fundamental fields, Ψ L ∼ (4 , 6 , 1) and Ψ R ∼ (4 , 1 , 6), thereby explaining the origin of three families of fermions. The SM Higgs, being electroweakly charged, necessarily becomes charged also under flavour when embedded in the UV model. It is therefore natural for its vacuum expectation value to couple only to the third family. The other components of the UV Higgs fields are presumed heavy. Extra scalars are needed to break this symmetry down to the SM, which can proceed via ‘flavour-deconstructed’ gauge groups; for instance, we propose a pattern Sp(6) L → ∏ i = 1 3 SU 2 L , i → SU 2 L $$ {\prod}_{i=1}^3\mathrm{SU}{(2)}_{L,i}\to \mathrm{SU}{(2)}_L $$ for the left-handed factor. When the heavy Higgs components are integrated out, realistic quark Yukawa couplings with in-built hierarchies are naturally generated without any further ingredients, if we assume the various symmetry breaking scalars condense at different scales. The CKM matrix that we compute is not a generic unitary matrix, but it can precisely fit the observed values.

Abstract Extensions of the minimal supersymmetric standard model (MSSM) gauge group abound in the literature. Several of these include an additional U(1) X gauge group. Chiral fermions’ charge assignments under U(1) X are constrained to cancel local anomalies in the extension and they determine the structure and phenomenology of it. We provide all anomaly-free charge assignments up to a maximum absolute charge of Q max = 10, assuming that the chiral superfield content of the model is that of the MSSM plus up to three Standard Model (SM) singlet superfields. The fermionic components of these SM singlets may play the rôle of right-handed neutrinos, whereas one of the scalar components may play the rôle of the flavon, spontaneously breaking U(1) X . Easily scanned lists of the charge assignments are made publicly available on Zenodo. For the case where no restriction is placed upon Q max, we also provide an analytic parameterisation of the general solution using simple techniques from algebraic geometry.

Abstract We present a novel construction for a Higgs-VEV sensitive (HVS) operator, which can be used as a trigger operator in cosmic selection models for the electroweak hierarchy problem. Our operator does not contain any degrees of freedom charged under the SM gauge symmetries, leading to reduced tuning in the resulting models. Our construction is based on the extension of a two Higgs doublet model (2HDM) with a softly broken approximate global D 8 symmetry (the symmetry group of a square). A cosmic crunching model based on our extended Higgs sector has only a percent level tuning corresponding to the usual little hierarchy problem. In large regions of parameter space the 2HDM is naturally pushed towards the alignment limit. A complete model requires the introduction of fermionic top partners to ensure the approximate D 8 symmetry in the fermion sector. We also show that the same extended Higgs sector can be used for a novel implementation of the seesaw mechanism of neutrino masses.

Abstract We study generalized symmetries in a simplified arena in which the usual quantum field theories of physics are replaced with topological field theories and the smooth structure with which the symmetry groups of physics are usually endowed is forgotten. Doing so allows many questions of physical interest to be answered using the tools of homotopy theory. We study both global and gauge symmetries, as well as ‘t Hooft anomalies, which we show fall into one of two classes. Our approach also allows some insight into earlier work on symmetries (generalized or not) of topological field theories.

Abstract Costa et al. [Phys. Rev. Lett. 123 (2019) 151601] recently gave a general solution to the anomaly equations for n charges in a U(1) gauge theory. ‘Primitive’ solutions of chiral fermion charges were parameterised and it was shown how operations performed upon them (concatenation with other primitive solutions and with vector-like solutions) yield the general solution. We show that the ingenious methods used there have a simple geometric interpretation, corresponding to elementary constructions in number theory. Viewing them in this context allows the fully general solution to be written down directly, without the need for further operations. Our geometric method also allows us to show that the only operation Costa et al. require is permutation. It also gives a variety of other, qualitatively similar, parameterisations of the general solution, as well as a qualitatively different (and arguably simpler) form of the general solution for n even.