Modern Physics Letters A

The hidden sector of the E₈×E′₈ heterotic superstring theory of Gross et al. can in principle contain additional "shadow" matter, interacting only gravitationally with the real world in which we live. The SU(3)′_C×SU(2)′_L×U(1)′_Y shadow configuration symmetric to the standard model has been ruled out by Kolb et al. from nucleosynthesis arguments, combined with the existence of three light neutrinos. In the absence of inflation and of entropy enhancement by the out-of-equilibrium decay of an unstable particle, the same exclusion applies to the unbroken E′₈ hidden gauge group, assuming thermodynamical equilibrium with the observable sector E₆ group, and consequently all breaking chains E′₈→ G₁×G₂×⋯, since they can only reduce the effective number of four-dimensional degrees of freedom g_eff. The hidden sector would then appear to be in its vacuum state, which implies the absence of all condensates as well, if their potentials are positive semi-definite. In this case, and if there is no anomalous U(1) symmetry in the observable sector, the QCD axion is the model-independent axion, whose decay constant (where is the strong-interaction coupling parameter) requires a fine-tuning of the initial value of this axion field to a_i/f_a≲3×10^-3, in order not to overclose the Universe today, supersymmetry being broken by gauge mediation. Vice versa, if a_i/f_a~1, then hidden-sector gaugino condensation is necessary for there to be a sufficiently massive gravitino, whose decay can increase the entropy. Astronomical microlensing observations may help to discriminate between these two cases.

In this letter, we discuss how some quantum algebraic structures can be realized in terms of 2-D fractional supersymmetry generators. In particular, we show that there is a kind of quantum w_∞-symmetry which induces the quantum enveloping U_t(sl(2)) algebra.

We consider a three-dimensional brane-universe moving in a type 0 string background. The motion induces on the brane a cosmological evolution which, for some range of the parameters, exhibits an inflationary phase.

Upper limits for the mass–radius ratio are derived for arbitrary general relativistic matter distributions in the presence of a cosmological constant. General restrictions for the redshift and total energy (including the gravitational contribution) for compact objects in the Schwarzschild–de Sitter geometry are also obtained in terms of the cosmological constant and of the mean density of the star.

The Casimir energy for scalar field of two parallel conductors in two-dimensional domain wall background, with Dirichlet boundary conditions, is calculated by making use of general properties of renormalized stress–tensor. We show that vacuum expectation values of stress–tensor contain two terms which come from the boundary conditions and the gravitational background. In two dimensions the minimal coupling reduces to the conformal coupling and stress–tensor can be obtained by the local and nonlocal contributions of the anomalous trace. This work shows that there exists a subtle and deep connection between Casimir effect and trace anomaly in curved space–time.

Under nonspherical coordinates, the free energy and the entropy of a scalar field are calculated in terms of the brick-wall method on the background of a nonasymptotically flat cylindrical black hole. It is shown that the entropy is not only related to the area of an outer horizon but also function of inner horizon at nonasymptotically flat space–time, when a black hole has both inner and outer horizons. Further, the entropy expressed by location parameter of outer and inner horizons approaches zero, when the radiation temperature of a black hole approaches zero. It satisfies the Nernst theorem and can be taken as Planck absolute entropy of a black hole.

We obtain the energy of a conformal scalar dyon black hole (CSD) by using the energy–momentum complexes of Tolman and Möller. The total gravitational energy is given by the CSD charge in both prescriptions.

We define a normalized Weyl-type ⋆-product on general Kähler manifolds. Expanding this product perturbatively we show that the cumbersome term, which appears in a Berezin-type product, does not appear at least in the first order of ℏ. This means a normalization factor, which is introduced by Reshetikhin and Takhtajan for a Berezin-type product, is unnecessary for our Weyl-type product at that order.