International Journal of Modern Physics A

We briefly review the status of motivated beyond-the-MSSM phenomenology in the light of the LHC searches to date. In particular, we discuss the conceptual consequences of the exclusion bounds, of the hint for a Higgs boson at about 125 GeV, and of interpreting the excess of direct CP violation in the charm sector as a signal of New Physics. We try to go into the various topics in a compact way while providing a relatively rich list of references, with particular attention to the most recent developments.

We introduce and study a class of non-Hermitian Hamiltonians which have velocity dependent potentials. Since stability cannot be advocated directly from the classical potential, we show that the energy spectra are real and bounded from below which proves the stability of the spectra of all members in the class. We find that the introduced class of non-Hermitian Hamiltonians do have a corresponding superpartner class of non-Hermitian Hamiltonians. We were able to introduce supercharges which in conjunction with the corresponding super Hamiltonians constitute a closed super algebra. Among the introduced Hamiltonians, we show that non--symmetric Hamiltonians can be transformed into their corresponding superpartner Hamiltonians via a specific canonical transformation while the -symmetric ones failed to be mapped to their corresponding superpartner Hamiltonians via the same canonical transformation. Since canonical transformations preserve the spectrum, we conclude that non--symmetric Hamiltonians out of the introduced class of Hamiltonians have the same spectrum as the corresponding superpartner Hamiltonians and thus supersymmetry (Susy) is broken for such Hamiltonians. This kind of intertwining of -symmetry and Susy is new as all the so far discussed cases concentrate on Hamiltonians of broken -symmetry that have broken Susy too while we showed that Susy can be also broken for non--symmetric and non-Hermitian Hamiltonians.

In noncommutative phase space, wave functions and energy spectra are derived for the three-dimensional (3D) Klein–Gordon oscillator in a background magnetic field. The raising and lowering operators for this system are derived from the Heisenberg equations of motion for a 3D nonrelativistic oscillator. The coherent states are obtained as the eigenstates of the lowering operators and it is found that the coherent states are not the minimum uncertainty states due to the noncommutativity of the space. It is also pointed out that in the semiclassical limit, quantum matrix elements give solutions to the semiclassical equations.

We calculate the decay rate of light scalar mesons, using a diquark chiral effective theory, recently proposed to describe exotic hadrons. In the effective theory the light scalar mesons are postulated to be bound states of diquark and antidiquark. We find our results are in good agreement with experimental data. The axial couplings of diquarks with pions and kaons are found to be quite small and the perturbation is reliable. It shows that the diquark picture captures the correct physics of light scalar mesons.

The internal 4-form field strengths with 7-dimensional indices have been constructed by de Wit and Nicolai in 1986. They are determined by the following six quantities: the 56-bein of 4-dimensional ${\mathcal N} = 8$ gauged supergravity, the Killing vectors on the round seven-sphere, the covariant derivative acting on these Killing vectors, the warp factor, the field strengths with 4-dimensional indices and the 7-dimensional metric.

In this paper, by projecting out the remaining mixed 4-form field strengths in an SU(8) tensor that appears in the variation of spin-½ fermionic sector, we also write down them explicitly in terms of some of the above quantities. For the known critical points, the ${\mathcal N} = 8$ $SO(8)$ point and the nonsupersymmetric SO(7)⁺ point, we reproduce the corresponding 11-dimensional uplifts by computing the full nonlinear expressions. Moreover, we find out the 11-dimensional lift of the nonsupersymmetric SO(7)⁺ invariant flow. We decode their implicit formula for the first time and the present work will provide how to obtain the new supersymmetric or nonsupersymmetric membrane flows in 11 dimensions.

-1 The boson images of fermion SO(2N+1) Lie operators have been given together with those of SO(2N+2) ones. The SO(2N+1) Lie operators are generators of rotation in the (2N+1)-dimensional Euclidean space (N: number of single-particle states of the fermions). The images of fermion annihilation–creation operators must satisfy the canonical anticommutation relations, when they operate on a spinor subspace. In the regular representation space we use a boson Hamiltonian with Lagrange multipliers to select out the spinor subspace. Based on these facts, a new description of a fermionic SO(2N+2) top is proposed. From the Heisenberg equations of motions for the boson operators, we get the SO(2N+1) self-consistent field (SCF) Hartree–Bogoliubov (HB) equation for the classical stationary motion of the fermion top. Decomposing an SO(2N+1) matrix into matrices describing paired and unpaired modes of fermions, we obtain a new form of the SO(2N+1) SCF equation with respect to the paired-mode amplitudes. To demonstrate the effectiveness of the new description based on the bosonization theory, the extended HB eigenvalue equation is applied to a superconducting toy-model which consists of a particle–hole plus BCS-type interaction. It is solved to reach an interesting and exciting solution which is not found in the traditional HB eigenvalue equation due to the unpaired-made effects. To complete the new description, the Lagrange multipliers must be determined in the classical limit. For this aim a quasi-anticommutation relation approximation is proposed. Only if a certain relation between an SO(2N+1) parameter z and the N is satisfied, unknown parameters K and l in the Lagrange multipliers can be determined without any inconsistency.

We study the contribution of the antisymmetric tensor unparticle mediation to the branching ratios of the radiative lepton flavor violating decays and predict a restriction region for free parameters of the scenario by using experimental upper limits. We observe that the branching ratios of the radiative lepton flavor violating decays are sensitive to the fundamental mass scales of the scenario and to the scale dimension of antisymmetric tensor unparticle. We obtain a more restricted set for the free parameters in the case of the μ→e γ decay.

We consider a total action composed of two Dirac–Born–Infeld (DBI) actions: one for a vector field A_μ and another for an axial vector field B_μ. We impose a duality condition , where is the Hodge dual of G_μν, and g is a DBI interaction constant. Interestingly, there are two different global duality rotation symmetries in the presence of DBI interactions: (i) , , and (ii) δ_ζA_μ = - ζB_μ, δ_ζB_μ = + ζA_μ. Both of these symmetry are on-shell symmetries, including nonlinear higher-order terms. The remarkable aspect is that these symmetries are valid even in the presence of DBI interactions. The coupling of this system to N = 1 supergravity is also discussed.

We propose two families of differential algebras of classical dimension on κ-Minkowski space. The algebras are constructed using realizations of the generators as formal power series in a Weyl superalgebra. We also propose a novel realization of the Lorentz algebra in terms of Grassmann-type variables. Using this realization we construct an action of on the two families of algebras. Restriction of the action to κ-Minkowski space is covariant. In contrast to the standard approach the action is not Lorentz covariant except on constant one-forms, but it does not require an extra cotangent direction.

This article was published as a part of the conference proceedings for the Eighth Alexander Friedmann International Seminar on Gravitation and Cosmology and Satellite Symposium on the Casimir Effect, held in Rio de Janeiro, Brazil, 30 May–3 June 2011. In the article I described results of the force obtained in the Casimir regime between a Au coated sphere and a Au grating. The making of the grating required extensive development from my collaborators. The article was published without the proper authorship from the research groups involved. Against this background I thus retract my article and apologize for the damage I have caused.