A relation between the Barbero–Immirzi parameter and the standard model

It has been shown that Sakharov's induced, from the fields entering the standard model, Barbero–Immirzi parameter γ assumes, in the framework of Euclidean formalism, the UV cutoff-independent value, 1/9. The calculus uses the Schwinger's proper-time formalism, the Seeley–DeWitt heat-kernel expansion, and it is akin to the derivation of the ABJ chiral anomaly in space–time with torsion.     

Einstein–Cartan gravity,Asymptotic Safety,and the running Immirzi parameter

In this paper we analyze the functional renormalization group flow of quantum gravity on the Einstein–Cartan theory space. The latter consists of all action functionals depending on the spin connection and the vielbein field (co-frame) which are invariant under both spacetime diffeomorphisms and local frame rotations. In the first part of the paper we develop a general methodology and corresponding calculational tools which can be used to analyze the flow equation for the pertinent effective average action for any truncation of this theory space. In the second part we apply it to a specific three-dimensional truncated theory space which is parametrized by Newton’s constant, the cosmological constant, and the Immirzi parameter. A comprehensive analysis of their scale dependences is performed, and the possibility of defining an asymptotically safe theory on this hitherto unexplored theory space is investigated. In principle Asymptotic Safety of metric gravity (at least at the level of the effective average action) is neither necessary nor sufficient for Asymptotic Safety on the Einstein–Cartan theory space which might accommodate different “universality classes” of microscopic quantum gravity theories. Nevertheless, we do find evidence for the existence of at least one non-Gaussian renormalization group fixed point which seems suitable for the Asymptotic Safety construction in a setting where the spin connection and the vielbein are the fundamental field variables.     

A new limit for the noncommutative space–time parameter

The spectrum of the hydrogen atom in the framework of noncommutative quantum mechanics is studied and the related phenomenology is presented. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in the atom. To the first order in the noncommutative parameter, it is equivalent to an electron in the fields of a Coulomb potential and an electric dipole and this allows us to get a bound for this parameter. In a second step, we compute noncommutative corrections of the energy levels and find that they are at the second order in the parameter of noncommutativity. By comparing our results to those obtained from experimental spectroscopy, we get another limit for this parameter.     

A note on γ traces for the Wilson action in the continuum limit

In d=4 and d=2 dimensions we calculate averages of certain products of matrices with respect to closed lattice paths of length L. The approach to the asymptotic behaviour for large L is considered and found to be quite different in d=4 and d=2 dimensions.Institute für Theoretische Physik der Universität Hamburg, F.R.G.     

A note on the M2–M5 brane system and fuzzy spheres

This note covers various aspects of recent attempts to describe membranes ending on fivebranes using fuzzy geometry. In particular, we examine the Basu–Harvey equation and its relation to the Nahm equation as well as the consequences of using a non-associative algebra for the fuzzy three-sphere. This produces the tantalising result that the fuzzy funnel solution corresponding to Q   coincident membranes ending on a five-brane has Q3/2$Q^{3/2}$ degrees of freedom.     

A note on the ‘one-link’ integral of U(N) lattice gauge theory

We calculate the one-link U(N) integral in closed form by a direct method, i.e., polar decomposition and integration over agular variables. The result agrees with the known solution of the Brower-Nauenberg equation, at least forN4.Notice that in Reference [7] a direct integration was given forN=2 andN=3 However, the identification with Equation (2) was not given explicity, but on the basis on the assumed uniqueness of the solution.     

A note on the UV behaviour of maximally supersymmetric Yang–Mills theories

The question of whether BPS invariants are protected in maximally supersymmetric Yang–Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants (F⁴$F^4$) are indeed protected while the double-trace one-quarter BPS invariant (d²F⁴$d^2{F}^4$) is not protected at two loops in D=7$D=7$, but is protected at three loops in D=6$D=6$ in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotected.     

A note on grey solitons of the cubic–quintic Schrödinger equation

Using the soliton solutions of the Boussinesq-like equation as brick materials, the one, two and three grey solitons of the nonlinear cubic–quintic nonlinear Schrödinger equation are constructed. We present the elastic and inelastic interaction of these solutions.     

Effects of annealing time on the structure,morphology, and stress of gold–chromium bilayer film

In this work, a 200-nm-thick gold film with a 10-nm-thick chromium layer used as an adhesive layer is fabricated on fused silica by the electron beam evaporation method. The effects of annealing time at 300℃ on the structure, morphology and stress of the film are studied. We find that chromium could diffuse to the surface of the film by formatting a solid solution with gold during annealing. Meanwhile, chromium is oxidized on the surface and diffused downward along the grain grooves in the gold film. The various operant mechanisms that change the residual stresses of gold films for different annealing times are discussed.     

A note on the Lie algebras g(m∞)

The algebras g(m) are interpreted as realisations of the infinite rank affine Lie algebras g.     

A possible minimal gauge–Higgs unification

A possible minimal model of the gauge–Higgs unification based on the higher dimensional spacetime M ⁴⊗(S ¹/Z ₂) and the bulk gauge symmetry SU(3) _C ⊗SU(3) _W ⊗U(1) _X is constructed in some detail. We argue that the Weinberg angle and the electromagnetic current can be correctly identified if one introduces the extra U(1) _X above and a bulk scalar triplet. The VEV of this scalar as well as the orbifold boundary conditions will break the bulk gauge symmetry down to that of the standard model. A new neutral zero-mode gauge boson Z′ exists that gains mass via this VEV. We propose a simple fermion content that is free from all the anomalies when the extra brane-localized chiral fermions are taken into account as well. The issues on recovering a standard model chiral-fermion spectrum with the masses and flavor mixing are also discussed, where we need to introduce the two other brane scalars which also contribute to the Z′ mass in the similar way as the scalar triplet. The neutrinos can get small masses via a type I seesaw mechanism. In this model, the mass of the Z′ boson and the compactification scale are very constrained being, respectively, given in the ranges: 2.7 TeV<m _Z′<13.6 TeV and 40 TeV<1/R<200 TeV.     

A note on the mass splitting of K*(892)

Belle Collaboration reported a new observed value of K*-(892) mass by studying τ- → KSπ-ντ decay, which is significantly different from the current world average value given by Particle Data Group 2006. Motivated by this new data, we revisit the issue on the K*0(892)-K*±(892) mass splitting. Our theoretical estimation favors the new measurement by Belle Collaboration. Therefore further experimental efforts are urgently needed to improve our understanding of these issues.     

Heat-kernel expansion and counterterms of the Faddeev–Popov determinant in Coulomb and Landau gauge

The Faddeev–Popov determinant of Landau gauge in d dimensions and Coulomb gauge in d+1 dimensions is calculated in the heat-kernel expansion up to next-to-leading order. The UV-divergent parts in d=3,4 are isolated and the counterterms required for a non-perturbative treatment of the Faddeev–Popov determinant are determined.     

A Dirac–Dunkl Equation on S2 and the Bannai–Ito Algebra

The Dirac–Dunkl operator on the two-sphere associated to the \({{\mathbb{Z}_{2}^{3}}}\) reflection group is considered. Its symmetries are found and are shown to generate the Bannai–Ito algebra. Representations of the Bannai–Ito algebra are constructed using ladder operators. Eigenfunctions of the spherical Dirac–Dunkl operator are obtained using a Cauchy–Kovalevskaia extension theorem. These eigenfunctions, which correspond to Dunkl monogenics, are seen to support finite-dimensional irreducible representations of the Bannai–Ito algebra.