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.     

The O(g) coefficient in the thermodynamic potential of hot SU(N) gauge theories and MQCD

The non-perturbative input necessary for the determination of the

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(g⁶) part of the weak coupling expansion of the free energy density for SU(2) and SU(3) gauge theories is estimated. Although the perturbative information completing the contribution to this order is missing, we give arguments that the magnetic fluctuations are dominated by screened elementary magnetic gluons.     

Study of the process ee→ππγ in c.m. energy range 600–970 MeV at CMD-2

The cross section of the process e⁺e⁻→π⁰π⁰γ has been measured in the c.m. energy range 600–970 MeV with the CMD-2 detector. The following branching ratios have been determined:

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and

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. Evidence for the ρ⁰→f₀(600)γ decay has been obtained:

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. From a search for the process e⁺e⁻→ηπ⁰γ the following upper limit has been obtained: at 90% CL.     

Correlator of the quark scalar currents and Γtot(H → hadrons) at O(αs) in pQCD

We present the results of the analytical evaluation of the massless four-loop

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(α³_s) correction to the correlator of the quark scalar currents and the Higgs decay rate into hadrons. In numerical form we found (in

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scheme) that Γ (H →

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b ) = (3G_F/4

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π) M_Hm²_b (M_H) [1 + 5.667α_s/π + (35.94 − 1.359n_f) (α_s/π)² + (164.139 − 25.771n_f + 0.259n²_f) (α_s/π)³] where n_f is the number of quark flavour and α_s = α_s(M_H).     

Four-dimensional high-branes as intersecting D-branes

We show that a class of external four-dimensional supersymmetric “high-branes”, i.e. string and domain wall solutions, can be interpreted as intersections of four ten-dimensional Dirichlet branes. These d = 4 solutions are related, via T-duality in ten dimensions, to the four-dimensional extermal Maxwell/scalar black holes that are characterized by a scalar coupling parameter a with a = 0,1

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, 1,

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.     

Coupled Hamiltonians and three-dimensional short-range wetting transitions

We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate

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(y) representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d = 3 at critical and complete wetting, respectively, which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau model. Building on earlier work by Parry and Boulter we investigate the hypothesis that these concerns arise due to the coupling of order parameter fluctuations near the unbinding interface and wall. For quite general choices of collective coordinates X_i(y) we show that arbitrary two-field models H[X₁,X₂] can recover the required anomalous structure of mean-field correlation functions (P3). To go beyond mean-field theory we introduce a set

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of Hamiltonians based on proper collective coordinates s(y) near the wall which have both interfacial and spin-like components. We argue that an optimum model H[s,

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]

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, in which the degree of coupling is controlled by an angle like variable δ^*, best describes the non-universality of the Ising model and investigate its critical behaviour. For critical wetting the appropriate Ginzburg criterion shows that the true asymptotic critical regime for the local susceptibility χ₁ is dramatically reduced consistent with observations of mean-field behaviour in simulations (P1). For complete wetting the model yields a precise expression for the temperature dependence of the renormalised critical amplitude θ in good agreement with simulations (P2). We highlight the importance of a new wetting parameter which describes the physics that emerges due to the coupling effects.     

Refractive indices of biaxial crystals evaluated from the refractive indices ellipsoid equation

The expressions of the refractive indices corresponding wave vector k(θ,) are given by using coordinate transformations for the refractive indices ellipsoid equation of biaxial crystals. The refractive index expression of the wave, whose velocity is slower, is given by

and that of the wave, whose velocity is faster, is given by

     

Behaviour of gluons at high temperature

The screening of colour electric and magnetic fields and plasma oscillations in a high-temperature gluon plasma are investigated using linear response theory and self-consistent nonperturbative solutions to the Schwinger-Dyson equation. Static electric fields are screened, with

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. This result is proven to be gauge invariant in two ways: by computing π₀₀ in temporal axial, Coulomb and covariant gauges, and by computing the physical free energy of a heavy quark pair in the plasma in temporal axial gauge. To order g³ static magnetic fields are not screened.     

Decay of Bc (3S) → B D

The decay constant for the vector state of 3S-level in the heavy (

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c)-quarkonium is evaluated in the framework of sum rules for the mesonic currents. A scaling relation for the constants of vector quarkonia with different quark contents is derived. The numerical estime gives Γ (B^*+_c(3S) → B⁺ D⁰) = 90 ± 35 MeV.     

Semileptonic decays B → (π, )eν in relativistic quark model

Quark model results for the B → π, decays are analysed, making use of the dispersion formulation of the model: The form factors at q² > 0 are expressed as relativistic invariant double spectral representation over invariant masses of the initial and final mesons through their light-cone wave functions. The dependence of the results on the quark model parameters is studied. For various versions of the quark model the ranges

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,

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, and Γ_L/Γ_T = 0.7 ± 0.08 are found. The effects of the constituent quark transition form factor are briefly discussed.     

Exact holography of the mass-deformed M2-brane theory

We test the holographic relation between the vacuum expectation values of gauge invariant operators in \({\mathcal {N}} = 6\) U\(_k(N)\times \mathrm{U}_{-k}(N)\) mass-deformed ABJM theory and the LLM geometries with \({\mathbb {Z}}_k\) orbifold in 11-dimensional supergravity. To do so, we apply the Kaluza–Klein reduction to construct a 4-dimensional gravity theory and implement the holographic renormalization procedure. We obtain an exact holographic relation for the vacuum expectation values of the chiral primary operator with conformal dimension \(\Delta = 1\), which is given by \(\langle {\mathcal {O}}^{(\Delta =1)}\rangle = N^{\frac{3}{2}} \, f_{(\Delta =1)}\), for large N and \(k=1\). Here the factor \(f_{(\Delta )}\) is independent of N. Our results involve an infinite number of exact dual relations for all possible supersymmetric Higgs vacua and so provide a non-trivial test of gauge/gravity duality away from the conformal fixed point. We extend our results to the case of \(k\ne 1\) for LLM geometries represented by rectangular-shaped Young diagrams. We also discuss the exact mapping of the gauge/gravity at finite N for classical supersymmetric vacuum solutions in field theory side and corresponding classical solutions in gravity side.