A modification of Einstein–Schrödinger theory that contains Einstein–Maxwell–Yang–Mills theory

The Lambda-renormalized Einstein–Schrödinger theory is a modification of the original Einstein–Schrödinger theory in which a cosmological constant term is added to the Lagrangian, and it has been shown to closely approximate Einstein– Maxwell theory. Here we generalize this theory to non-Abelian fields by letting the fields be composed of d × d Hermitian matrices. The resulting theory incorporates the U(1) and SU(d) gauge terms of Einstein–Maxwell–Yang–Mills theory, and is invariant under U(1) and SU(d) gauge transformations. The special case where symmetric fields are multiples of the identity matrix closely approximates Einstein–Maxwell–Yang–Mills theory in that the extra terms in the field equations are < 10^?13 of the usual terms for worst-case fields accessible to measurement. The theory contains a symmetric metric and Hermitian vector potential, and is easily coupled to the additional fields of Weinberg–Salam theory or flipped SU(5) GUT theory. We also consider the case where symmetric fields have small traceless parts, and show how this suggests a possible dark matter candidate.     

<Emphasis Type="Italic">SU</Emphasis>(2|1) supersymmetric mechanics as a deformation of <Emphasis Type="Italic">N</Emphasis> = 4 mechanics

We give a brief review of SU(2|1) supersymmetric quantum mechanics based on the worldline realizations of the supergroup SU(2|1) in the appropriate N = 4, d = 1 superspaces. The corresponding SU(2|1) models are deformations of standard N = 4, d = 1 models by a mass parameter m.     

The trinification model <Emphasis Type="Italic">SU</Emphasis>(3)<Superscript>3</Superscript> from orbifolds for fuzzy spheres

In this review, we consider an N = 4 supersymmetric SU(3N) gauge theory defined on the Minkowski spacetime. Then we apply an orbifold projection leading to an N = 1 supersymmetric SU(N)³ model, with a truncated particle spectrum. Then, we present the dynamical generation of (twisted) fuzzy spheres as vacuum solutions of the projected field theory, breaking the SU(N)³ spontaneously to a chiral effective theory with unbroken gauge group the trinification group, SU(3)³.     

Relations between the electromagnetic form factors of the 0−- and 1−-mesons from the collinear groupsSU(3)⊗SU(3)⊗U(1) andSU(6) W

The relations between the electromagnetic matrix elements of the 18 low lying pseudoscalar and vector mesons predicted by the collinear groupsSU(3)?SU(3)?U(1) andSU(6) _W are derived. Using the hermiticity of the electromagnetic current operator, charge conjugation invariance and invariance under the full Lorentz group andSU(3)-symmetry separately, all electromagnetic matrix elements of these mesons are described by seven independent real form factors. After combining space-time with intrinsic properties of the particles this number is reduced to four by the minimal collinear groupSU(3) ?SU(3) ?U(1) and to three bySU(6) _W which involves more speculative assumptions. In the limit of low momentum transfer the predictions of both models become identical, depending on three real quantities. No disagreement with experiment has been found, as far as a comparison is possible.     

Monopoles and family-replicated unification

The present theory is based on the assumption that, at very small (Planck scale) distances our spacetime is discrete, and this discreteness influences the Planck scale physics. Considering our (3+1)-dimensional spacetime as a regular hypercubic lattice with a parameter a=λ_Pl, where λ_Pl is the Planck length, we have investigated a role of lattice artifact monopoles, which is essential near the Planck scale if the family-replicated gauge group model (FRGGM) is an extension of the Standard Model (SM) at high energies. It was shown that monopoles have N times smaller magnetic charge in the FRGGM than in the SM (N is the number of families in the FRGGM). These monopoles can give an additional contribution to β functions of the renormalization-group equations for the running fine structure constants α_i(μ) (i=1, 2, 3 correspond to the U(1), SU(2), and SU(3) gauge groups of the SM). We have used the Dirac relation for renormalized electric and magnetic charges. Also, we have estimated the enlargement of a number of fermions in the FRGGM leading to the suppression of the asymptotic freedom in the non-Abelian theory. The different role of monopoles in the vicinity of the Planck scale gives rise either to anti-GUT or to the new possibility of unification of gauge interactions (including gravity) at the scale μ_GUT≈10^18.4 GeV. We discussed the possibility of the [SU(5)]³ SUSY or [SO(10)]³ SUSY unifications.     

Dirac monopoles embedded in <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory with the θ term

Dirac monopoles embedded in SU(N) gauge theory with the θ term are considered. For θ=4πM (where M is half-integer and integer for N=2 and N>2, respectively), these monopoles acquire an SU(N) charge due to the θ term and become dyons. They belong to various (but not any) irreducible representations of the SU(N) group. The admissible representations are listed. Their minimum dimension increases with N. The basic result of the study is the representation of the partition function of any SU(N) model involving the θ term and complemented by singular gauge fields corresponding to the indicated monopoles in the form of a vacuum average of the product of Wilson loops viewed along the world lines of the monopoles. This vacuum average must be calculated in the corresponding model without the θ term.     

Constraints on <Emphasis Type="Italic">SU</Emphasis>(2) ⊗ <Emphasis Type="Italic">SU</Emphasis>(2) invariant polynomials for a pair of entangled qubits

We discuss the entanglement properties of two qubits in terms of polynomial invariants of the adjoint action of SU(2) ⊕ SU(2) group on the space of density matrices \(\mathfrak{P}_ +\). Since elements of \(\mathfrak{P}_ +\) are Hermitian, non-negative fourth-order matrices with unit trace, the space of density matrices represents a semi-algebraic subset, \(\mathfrak{P}_ + \in \mathbb{R}^{15}\). We define \(\mathfrak{P}_ +\) explicitly with the aid of polynomial inequalities in the Casimir operators of the enveloping algebra of SU(4) group. Using this result the optimal integrity basis for polynomial SU(2) ⊕ SU(2) invariants is proposed and the well-known Peres-Horodecki separability criterion for 2-qubit density matrices is given in the form of polynomial inequalities in three SU(4) Casimir invariants and two SU(2) ⊕ SU(2) scalars; namely, determinants of the so-called correlation and the Schlienz-Mahler entanglement matrices.     

The discrete family symmetries as the possible solution to the flavour problem

In order to explain the fermions’ masses and mixing parameters appearing in the lepton sector of the Standard Model, one proposes the extension of its symmetry. A discrete, non-Abelian subgroup of U(3) is added to the gauge group SU(3) _C × SU(2) _L × U(1) _Y . Apart from that, one assumes the existence of one extra Higgs doublet. This article focuses mainly on the mathematical theorems and computational techniques which brought us to the results.     

Quark diagram analysis of <Emphasis Type="Italic">B</Emphasis>-meson emitting vector (<Emphasis Type="Italic">V</Emphasis>) and vector (<Emphasis Type="Italic">V</Emphasis>) mesons

This paper presents the two body weak nonleptonic decays of B-mesons emitting vector (V) and vector (V) mesons within the framework of the diagrammatic approaches at flavor SU(3) symmetry. We have investigated exclusive two body decays of B-meson using model independent quark diagram scheme. We have shown that the recent measurement of the two body exclusive decays of B-mesons can allow us to determine the magnitude and even sign of the QD amplitude for B → VV decays. Therefore, we become able to make few predictions for their branching fractions.     

<Emphasis Type="Italic">SU</Emphasis>(2)×<Emphasis Type="Italic">SU</Emphasis>(2) chiral quark model with nonlocal interaction

Masses and interactions of light mesons are described in the framework of the model with the chiral invariant SU(2)×SU(2) four-quark interaction. The nonlocal kernel of the interaction is chosen in the form that ensures the absence of ultraviolet divergences in the Feynman diagrams and poles in the quark propagator. Within this model, we demonstrate that, in the chiral limit, the pion mass equals zero and the Goldberger-Treiman relation is fulfilled. The sigma-meson mass and the widths of strong decays σ → ππ, ρ → νν are estimated.     

Charge-exchange resonances and restoration of Wigner’s supersymmetry in heavy and superheavy nuclei

Various facets of the question of whether Wigner’s supersymmetry [SU(4) symmetry] may be restored in heavy and superheavy nuclei are analyzed on the basis of a comparison of the results of calculations with experimental data. The energy difference between the giant Gamow–Teller resonance and the analog resonance (the difference of E _G and E _A) according to calculations based on the theory of finite Fermi systems is presented for the case of 33 nuclei for which experimental data are available. The calculated difference ΔE _G–A of E _G and E _A tends to zero in heavier nuclei, showing evidence of the restoration of Wigner’s SU(4) symmetry. Also, the isotopic dependence of the Coulomb energy difference between neighboring isobaric nuclei is analyzed within the SU(4) approach for more than 400 nuclei in the mass-number range of A = 5–244. The restoration of Wigner’s SU(4) symmetry in heavy nuclei is confirmed. It is shown that the restoration of SU(4) symmetry is compatible with the possible existence of the stability island in the region of superheavy nuclei.     

Massive hyper-Kähler sigma models and BPS domain walls

With the non-Abelian hyper-Kähler quotient by U(M) and SU(M) gauge groups, we give the massive hyper-Kähler sigma models that are not toric in the N=1 superfield formalism. The U(M) quotient gives N!/[M!(N-M)!] (N is the number of flavors) discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua. We derive a BPS domain-wall solution in the case of N = 2 and M = 1 in the U(M) quotient model.     

An additional symmetry in the Weinberg-Salam model

An additional Z₆ symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently. It has a singular nature and is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In this paper, we report our results on the numerical simulation of its electroweak sector.     

Process <Emphasis Type="Italic">γ</Emphasis>*<Emphasis Type="Italic">γ</Emphasis> → <Emphasis Type="Italic">σ</Emphasis> at large virtuality of <Emphasis Type="Italic">γ</Emphasis>*

The process γ*γ → σ is investigated in the framework of the SU(2)×SU(2) chiral NJL model. The form factor of the process is derived for arbitrary virtuality of γ* in the Euclidean kinematic domain. The asymptotic behavior of this form factor resembles the asymptotic behavior of the γ*γ → π form factor.     

Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

Emergent nesting of the Fermi surface from local-moment description of iron-pnictide high-T<Subscript>c</Subscript> superconductors

We uncover the low-energy spectrum of a t-J model for electrons on a square lattice of spin-1 iron atoms with 3d _xz and 3d _yz orbital character by applying Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of one hole roaming over a 4 × 4 × 2 lattice. Hopping matrix elements are set to produce hole bands centered at zero two-dimensional (2D) momentum in the free-electron limit. Holes can propagate coherently in the t-J model below a threshold Hund coupling when long-range antiferromagnetic order across the d + = 3d _{(x + iy)z} and d ? = 3d _{(x ? iy)z} orbitals is established by magnetic frustration that is off-diagonal in the orbital indices. This leads to two hole-pocket Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate spin-density wave (cSDW) that exists above the threshold Hund coupling results in emergent Fermi surface pockets about cSDW momenta at a quantum critical point (QCP). This motivates the introduction of a new Gutzwiller wavefunction for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta indicates that the dispersion of the nested band of one-particle states that emerges is electron-type. Increasing Hund coupling past the QCP can push the hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy level, in agreement with recent determinations of the electronic structure of mono-layer iron-selenide superconductors.     

AdS branes from partial breaking of superconformal symmetries

It is shown how the static-gauge world-volume superfield actions of diverse superbranes on the AdS_d+1 superbackgrounds can be systematically derived from nonlinear realizations of the appropriate AdS supersymmetries. The latter are treated as superconformal symmetries of flat Minkowski superspaces of the bosonic dimension d. Examples include the N = 1 AdS₄ supermembrane, which is associated with the 1/2 partial breaking of the OSp(1|4) supersymmetry down to the N = 1, d = 3 Poincaré supersymmetry, and the T-duality related L3-brane on AdS₅ and scalar 3-brane on AdS₅ × S¹, which are associated with two different patterns of 1/2 breaking of the SU(2, 2|1) supersymmetry. Another (closely related) topic is the AdS/CFT equivalence transformation. It maps the world-volume actions of the codimension-one AdS_d+1 (super)branes onto the actions of the appropriate Minkowski (super)conformal field theories in the dimension d.     

Rare kaon decay $$K^ + \to \pi ^ + \nu \bar \nu $$ in S U(3)C ⊗ S U(3)L ⊗ U(1)N models

The rare kaon decay \(K^ + \to \pi ^ + \nu \bar \nu \) is considered in the framework of models based on the SU(3) _C ? SU(3) _L ? U(1) _N (3-3-1) gauge group. In the 3-3-1 model with right-handed neutrinos, the lower bound of the Z’ mass is derived at 3 TeV, and that in the minimal version, at 1.7 TeV.     

Spacetime symplectic extension

It is conjectured that in the origin of spacetime there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l, C), l≥1 instead of the pseudoorthogonal one SO(1, d?1), d≥4 is proposed as the spacetime local structure group. A discrete sequence of the metric spacetimes of the fixed dimensionalities d=(2l)² and signatures, with l(2l?1) timelike and l(2l+1) spacelike directions, defined over the set of Hermitian second-rank spin tensors, is considered as an alternative to the pseudo-Euclidean extra dimensional spacetimes. The basic concepts of the symplectic framework are developed in general, and the ordinary and next-to-ordinary spacetime cases with l=1, 2, respectively, are elaborated in more detail. In particular, the scheme provides the rationale for the four-dimensionality and 1+3 signature of the ordinary spacetime.