SU Family Research Articles

Tri-unification: a separate SU(5) for each fermion family

In this paper we discuss SU(5)3 with cyclic symmetry as a possible grand unified theory (GUT). The basic idea of such a tri-unification is that there is a separate SU(5) for each fermion family, with the light Higgs doublet(s) arising from the third family SU(5), providing a basis for charged fermion mass hierarchies. SU(5)3 tri-unification reconciles the idea of gauge non-universality with the idea of gauge coupling unification, opening the possibility to build consistent non-universal descriptions of Nature that are valid all the way up to the scale of grand unification. As a concrete example, we propose a grand unified embedding of the tri-hypercharge model \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext{U}}{\\left(1\\right)}_{Y}^{3}$$\\end{document} based on an SU(5)3 framework with cyclic symmetry. We discuss a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters. We show that it is possible to unify the many gauge couplings into a single gauge coupling associated with the cyclic SU(5)3 gauge group, by assuming minimal multiplet splitting, together with a set of relatively light colour octet scalars. We also study proton decay in this example, and present the predictions for the proton lifetime in the dominant e+π0 channel.

Review of Remote Consultations in Learning Disability During COVID Pandemic

AimsThe aim of this project was to assess the efficacy of remote consultations in patients with Learning Disability (LD). In Aneurin Bevan University Health Board, teleconsultation or “Attend Anywhere” (Video) platforms are the two types of remote consultation that is being offered.MethodsA 9- point Questionnaire was used to assess the efficiency of the consultation. During consultation (Either telephone or attend anywhere), data were collected by the consultants by answering the questionnaire. 23 clinics organised between 04/06/2020 to 23/06/2020 for Service Users' (SU) follow-up.The following key points were covered in the questionnaire: 1.Mode of consultation- telephone or attend anywhere2.Presence of the SU3.Introduction4.Availability of information (patient notes/shared drives) prior to consultation5.Time constraints6.Information not covered due to lack of face-to-face consult7.Technical difficulties8.Expectations from SU9.Feedback from SUResults1.The most common mode of consultation was via telephone (70%), followed by Attend Anywhere (30%)2.The majority of conversations were with SU's family or carers (70%); consultations with SU were only 30%. SU were unable to attend the consultation due to: Communication difficulty (26%), follow-ups provided by carer's/family's feedback (21.7%), SU away due to physical health reasons, or in day care (17.3%).3.Introductions were done and sufficient information regarding the service users were available in all consultations.4.Expectation of SU/carers/family was with regards to medication review (43%).5.52% of remote consultation were disrupted due to technical problems, for instance call drops and line disruptions, microphone issues and SU not being able to use attend anywhere because of its complexity.ConclusionIt was demonstrated that remote consultation could possibly be most effective for medication reviews or regular follow-up appointments.Some of the aspects that were not covered due to the shortcomings of remote consultations were: a.Difficulty in assessing body language and facial expressionsb.Difficulty in assessing the level of function of SUc.Unable to monitor physical health parametersd.Difficulty in picking up non-verbal cues, and assess eye contact to ascertain mood component of presentation.In summary it seems in the early stages of the pandemic, telephone consultation was the predominant form of remote consultation. Further work would be useful to obtain the views of people with LD, their carers and families as to which form of consultation would be their preference and whether remote consultation is acceptable for this patient group.

Large neutrino magnetic moments in the light of recent experiments

The excess in electron recoil events reported recently by the XENON1T experiment may be interpreted as evidence for a sizable transition magnetic moment {mu}_{v_e{v}_{mu }} of Majorana neutrinos. We show the consistency of this scenario when a single component transition magnetic moment takes values {mu}_{v_e{v}_{mu }}in left(1.65-3.42right)times {10}^{-11}{mu}_B . Such a large value typically leads to unacceptably large neutrino masses. In this paper we show that new leptonic symmetries can solve this problem and demonstrate this with several examples. We first revive and then propose a simplified model based on SU(2)H horizontal symmetry. Owing to the difference in their Lorentz structures, in the SU(2)H symmetric limit, mν vanishes while {mu}_{v_e{v}_{mu }} is nonzero. Our simplified model is based on an approximate SU(2)H, which we also generalize to a three family SU(3)H-symmetry. Collider and low energy tests of these models are analyzed. We have also analyzed implications of the XENON1T data for the Zee model and its extensions which naturally generate a large {mu}_{v_e{v}_{mu }} with suppressed mν via a spin symmetry mechanism, but found that the induced {mu}_{v_e{v}_{mu }} is not large enough to explain recent data. Finally, we suggest a mechanism to evade stringent astrophysical limits on neutrino magnetic moments arising from stellar evolution by inducing a medium-dependent mass for the neutrino.

Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice

We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (i.e., self-conjugate $\mathbf{6}$ representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimerlike phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauth\'e, S. Capponi, and D. Poilblanc, Phys. Rev. B 99, 241112(R) (2019)], we investigate the possibility of the existence of SU(4) quantum spin liquid phases in this model, using SU(4)-symmetric projected entangled pair states (PEPS) of small bond dimensions, which can be classified according to point group and charge (C) symmetries. Among several (disconnected) families of SU(4)-symmetric PEPS, breaking or not C-symmetry, we identify critical or topological spin liquids which may be stable in some regions of the phase diagram. These results are confronted to exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations.

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the J_1-J_2J1−J2 frustrated Heisenberg model. For J_2/J_1\sim 0.55J2/J1∼0.55 we show the emergence of critical (algebraic) dimer-dimer correlations – typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices – while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.

Novel families of SU(N) AKLT states with arbitrary self-conjugate edge states

Using the Matrix Product State framework, we generalize the Affleck-Kennedy-Lieb-Tasaki (AKLT) construction to one-dimensional spin liquids with global color SU(N) symmetry, finite correlation lengths, and edge states that can belong to any self-conjugate irreducible representation (irrep) of SU(N). In particular, SU(2) spin-1 AKLT states with edge states of arbitrary spin s=1/2,1,3/2,⋯ are constructed, and a general formula for their correlation length is given. Furthermore, we show how to construct local parent Hamiltonians for which these AKLT states are unique ground states. This enables us to study the stability of the edge states by interpolating between exact AKLT Hamiltonians. As an example, in the case of spin-1 physical degrees of freedom, it is shown that a quantum phase transition of central charge c=1 separates the Symmetry Protected Topological (SPT) phase with spin-1/2 edge states from a topologically trivial phase with spin-1 edge states. We also address some specificities of the generalization to SU(N) with N>2, in particular regarding the construction of parent Hamiltonians. For the AKLT state of the SU(3) model with the 3-box symmetric representation, we prove that the edge states are in the 8-dimensional adjoint irrep, and for the SU(3) model with adjoint irrep at each site, we are able to construct two different reflection-symmetric AKLT Hamiltonians, each with a unique ground state which is either even or odd under reflection symmetry and with edge states in the adjoint irrep. Finally, examples of two-column and adjoint physical irreps for SU(N) with N even and with edge states living in the antisymmetric irrep with N/2 boxes are given, with a conjecture about the general formula for their correlation lengths.

Wspomnienia z życia rodziny Stankiewiczów na Łotwie Sowieckiej

Jadwiga Radzynia, Memories about the Stankiewicz Family Life in Soviet LatviaThe article provides an account of the history of a family of noble background (bearing the Mogiła coat-of-arms), who had lived in Soviet Latvia for a number of generations. The family was put to test on numerous occasions by various governments. In the Soviet times its members, despite the risk of being considered “enemies of the nation”, kept their personal documents, family photograph albums, letters from Siberia and documents concerning their personal assets. It is the Soviet period that the most painful memories are connected with. The grandparents were considered “kulaks”. The family su´ered from imprisonment, exile to Siberia and continuous persecution, enforced collectivization and abolition of private economy. Like other national minorities and Latvians themselves, Poles living in Latvia experienced the process of russification and sovietization. Âe parents made every e´ort to adapt to the realities of contemporary life. Because they adhered to their Catholic faith, their Polish culture, their native language and parental love they retained their national identity and the sense of connection with their homeland, in which they lived. In 1991, after Latvian independence was proclaimed, the Stankiewicz family – as Poles living in Latvia for generations – did not find it difficult to adapt to the new situation and receive citizenship.

Marginal deformations & rotating horizons

Motivated by the near-horizon geometry of four-dimensional extremal black holes, we study a disordered quantum mechanical system invariant under a global SU(2) symmetry. As in the Sachdev-Ye-Kitaev model, this system exhibits an approximate SL(2, ℝ) symmetry at low energies, but also allows for a continuous family of SU(2) breaking marginal deformations. Beyond a certain critical value for the marginal coupling, the model exhibits a quantum phase transition from the gapless phase to a gapped one and we calculate the critical exponents of this transition. We also show that charged, rotating extremal black holes exhibit a transition when the angular velocity of the horizon is tuned to a certain critical value. Where possible we draw parallels between the disordered quantum mechanics and charged, rotating black holes.

A direct proof of dimerization in a family of SU(n)-invariant quantum spin chains

We study the family of spin-S quantum spin chains with a nearest neighbor interaction given by the negative of the singlet projection operator. Using a random loop representation of the partition function in the limit of zero temperature and standard techniques of classical statistical mechanics, we prove dimerization for all sufficiently large values of S.

Super-quantum states in SU(2) invariant [formula omitted] level systems

Nonclassicality of quantum states is expressed in many shades, one of the most stringent of them being a new standard introduced recently in Bharath and Ravishankar (2014), by expanding the notion of local hidden variables (LHV) to generalised local hidden variables (GLHV). Considering the family of SU(2) invariant 3×N level systems, we identify those states that do not admit a GLHV description, which we designate as super-quantum (called exceptional in Bharath and Ravishankar (2014). We show that all super-quantum states admit a universal geometrical description, and that they are most likely to lie on a line segment in the manifold, irrespective of the value of N. We also show that though a super-quantum state can be highly mixed, its relative rank with respect to the uniform state is always less than that of a state which admits a GLHV description.

Orbifold family unification on six dimensions

We study the possibility of family unification on the basis of SU(N) gauge theory on the 6-dimensional space-time, $M^4\times T^2/Z_N$. We obtain enormous numbers of models with three families of SU(5) matter multiplets and those with three families of the standard model multiplets, from a single massless Dirac fermion with a higher-dimensional representation of SU(N), through the orbifold breaking mechanism.

Solitons and Yukawa couplings in nearly Kähler flux compactifications

We study vacuum states and symmetric fermions in equivariant dimensional reduction of Yang-Mills-Dirac theory over the six-dimensional homogeneous space SU(3)/U(1)x U(1) endowed with a family of SU(3)-structures including a nearly Kahler structure. We derive the fixed tree-level scalar potentials of the induced Yang-Mills-Higgs theory, and compute the dynamically generated gauge and Higgs boson masses as functions of the metric moduli of the coset space. We find an integrable subsector of the Higgs field theory which is governed by a sine-Gordon type model whose topological soliton solutions are determined nonperturbatively by the gauge coupling and which tunnel between families of infinitely degenerate vacua. The reduction of the Dirac action for symmetric fermions yields exactly massless chiral fermions, containing subsectors which have fixed tree-level Yukawa interactions. We compute dynamical fermion mass matrices explicitly and compare them at differents points of the moduli space, some of which support consistent heterotic flux vacua.

Double quiver gauge theory and nearly Kähler flux compactifications

We consider G-equivariant dimensional reduction of Yang-Mills theory with torsion on manifolds of the form MxG/H where M is a smooth manifold, and G/H is a compact six-dimensional homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures which includes a nearly Kahler structure. We establish an equivalence between G-equivariant pseudo-holomorphic vector bundles on MxG/H and new quiver bundles on M associated to the double of a quiver Q, determined by the SU(3)-structure, with relations ensuring the absence of oriented cycles in Q. When M=R^2, we describe an equivalence between G-invariant solutions of Spin(7)-instanton equations on MxG/H and solutions of new quiver vortex equations on M. It is shown that generic invariant Spin(7)-instanton configurations correspond to quivers Q that contain non-trivial oriented cycles.

Quantifying uncertainty in statistical distribution of small sample data using Bayesian inference of unbounded Johnson distribution

Probabilistic analysis of physical systems requires information on the distributions of random variables. Distributions are typically obtained from testing or field data. In engineering design where tests are expensive, the sample size of such data is small O(10). Identifying correct distributions with small number of samples is difficult. Furthermore, parameters of assumed distributions obtained from small sample data themselves contain some uncertainty. In this study a Johnson SU family distribution function is used to identify shape, location and scale parameters of distribution that can best fit small sample data. A Bayesian inference procedure is used to determine distributions of the parameters. We show that the procedure correctly bounds the tail regions of the distributions and is less conservative than bounds obtained using bootstrap methods.

Non-Abelian Vortices, Super Yang–Mills Theory and Spin(7)-Instantons

We consider a complex vector bundle $${\mathcal{E}}$$ endowed with a connection $${\mathcal{A}}$$ over the eight-dimensional manifold $${\mathbb{R}^2\times G/H}$$ , where G/H = SU(3)/U(1) × U(1) is a homogeneous space provided with a never-integrable almost-complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions $${\mathcal{A}}$$ of the Spin(7)-instanton equations on $${\mathbb{R}^2\times G/H}$$ and general solutions of non-Abelian coupled vortex equations on $${\mathbb{R}^2}$$ . These vortices are BPS solitons in a d = 4 gauge theory obtained from $${\mathcal{N} =1}$$ supersymmetric Yang–Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over $${\mathbb{R}^2}$$ , are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in $${\mathcal{N} =4}$$ super Yang–Mills theory and show that they have the same feature.

Family unification, exotic states and light magnetic monopoles

Models with fermions in bifundamental representations can lead naturally to family unification as opposed to family replication. Such models typically predict (exotic) color singlet states with fractional electric charge, and magnetic monopoles with multiple Dirac charge. The exotics may be at the TeV scale, and relatively light magnetic monopoles (greater than about 10^7 GeV) can be present in the galaxy with abundance near the Parker bound. We focus on three family SU(4)XSU(3)XSU(3) models.

Standard model compactifications of IIA [formula omitted] orientifolds from intersecting D6-branes

We discuss the construction of chiral four-dimensional T 6 / ( Z 3 × Z 3 ) orientifold compactifications of IIA theory, using D6-branes intersecting at angles and not aligned with the orientifold O6 planes. Cancellation of mixed U ( 1 ) anomalies requires the presence of a generalized Green–Schwarz mechanism mediated by RR partners of closed string untwisted moduli. In this respect we describe the appearance of three quark and lepton family SU ( 3 ) C × SU ( 2 ) L × U ( 1 ) Y non-supersymmetric orientifold models with only the massless spectrum of the SM at low energy that can have either no exotics present and three families of ν R 's ( A ′ -model class) or the massless fermion spectrum of the N = 1 SM with a small number of massive non-chiral colour exotics and in one case with extra families of ν R 's ( B ′ -model class). Moreover we discuss the construction of SU ( 5 ) , flipped SU ( 5 ) and Pati–Salam SU ( 4 ) c × SU ( 2 ) L × SU ( 2 ) R GUTS—the latter also derived from adjoint breaking—with only the SM at low energy. Some phenomenological features of these models are also briefly discussed. All models are constructed with the Weinberg angle to be 3 / 8 at the string scale.

SPECIAL LAGRANGIAN CYCLES AND HERMITIAN YANG–MILLS CONNECTIONS

We consider the adiabatic limit of a sequence of Hermitian Yang–Mills connections on a SU(r)-bundle over a semi-flat smooth special Lagrangian torus fibration π:M→B. The restriction of these connections to the fiber tori can be viewed as a family of SU(r)-connections on the fiber tori which are parameterized by B. We show that there is a gauge equivalent subsequence such that the restriction of each connection to the fiber tori converges in the Hausdorff topology, away from some closed subset of B of codimension at least two, to a limit which defines a r-sheeted special Lagrangian cycle in the dual special Lagrangian torus fibration.

Supersymmetric three family SU(5) grand unified models from type IIA orientifolds with intersecting D6-branes

We construct some N=1 supersymmetric three-family SU(5) grand unified models from type IIA orientifolds on T 6/( Z 2× Z 2) with D6-branes intersecting at general angles. These constructions are supersymmetric only for special choices of untwisted moduli. We show that within the above class of constructions there are no supersymmetric three-family models with 3 copies of 10-plets unless there are simultaneously some 15-plets. We systematically analyze the construction of such models and their spectra. The M-theory lifts of these brane constructions become purely geometrical backgrounds: they are singular G 2 manifolds where the grand unified gauge symmetries and three families of chiral fermions are localized at codimension 4 and codimension 7 singularities respectively. We also study some preliminary phenomenological features of the models.

A MINIMAL SUPERSTRING STANDARD MODEL I: FLAT DIRECTIONS

Three family SU (3)C× SU (2)L× U (1)Y string models in several constructions generically possess two features: (i) an extra local anomalous U (1)A and (ii) numerous (often fractionally charged) exotic particles beyond those in the minimal supersymmetric model (MSSM). Recently, we demonstrated that the observable sector effective field theory of such a free fermionic string model can reduce to that of the MSSM, with the standard observable gauge group being just SU (3)C× SU (2)L× U (1)Y and the SU (3)C× SU (2)L× U (1)Y-charged spectrum of the observable sector consisting solely of the MSSM spectrum. An example of a model with this property was shown. We continue our investigation of this model by presenting a large set of different flat directions of the same model that all produce the MSSM spectrum. Our results suggest that even after imposing the conditions for the decoupling of exotic states, there may remain sufficient freedom to satisfy the remaining phenomenological constraints imposed by the observed data.