Modern Physics Letters A

We consider the interplay of duality symmetries and gauged isometries of supergravity models giving N-extended, spontaneously broken supergravity with a no-scale structure. Some examples motivated by superstring and M-theory compactifications are described.

New finite-dimensional representations of specific polynomial deformations of sl(2, ℝ) are constructed. The corresponding generators can be, in particular, realized through linear differential operators preserving a finite-dimensional subspace of monomials. We concentrate on three-dimensional spaces.

On the basis of the Berkovits pure spinor formalism of covariant quantization of supermembrane, we attempt to construct a M(atrix) theory which is covariant under SO(1, 10) Lorentz group. We first construct a bosonic M(atrix) theory by starting with the first-order formalism of bosonic membrane, which precisely gives us a bosonic sector of M(atrix) theory by BFSS. Next we generalize this method to the construction of M(atrix) theory of supermembranes. However, it seems to be difficult to obtain a covariant and supersymmetric M(atrix) theory from the Berkovits pure spinor formalism of supermembrane because of the matrix character of the BRST symmetry. Instead, in this paper, we construct a supersymmetric and covariant matrix model of 11D superparticle, which corresponds to a particle limit of covariant M(atrix) theory. By an explicit calculation, we show that the one-loop effective potential is trivial, thereby implying that this matrix model is a free theory at least at the one-loop level.

Traditional derivations of the Planck mass ignore the role of charge and spin in general relativity. From the Kerr–Newman null surface and horizon radii, quantized charge and spin dependence are introduced in an extended Planck scale of mass. Spectra emerge with selection rules dependent upon the choice of Kerr–Newman radius to link with the Compton wavelength. The appearance of the fine structure constant suggests the possibility of a variation in time of the extended Planck mass, which may be much larger than the variation in the traditional one. There is a suggestion of a connection with the α value governing high-energy radiation in Z-boson production and decay.

We show that the action of Einstein's gravity with a scalar field coupled in a generic way to spacetime curvature is invariant under a particular set of conformal transformations. These transformations relate dual theories for which the effective couplings of the theory are scaled uniformly. In the simplest case, this class of dualities reduces to the S-duality of low-energy effective action of string theory.

In this paper, we study the open string modes, describing the world-volume of a D p-brane, for its cyclic symmetry in the presence of a magnetic field. We outline the analogy between cyclic and noncommutative symmetries and demonstrate the point-splitting prescription to explain some of the unusual ir phenomena observed in a noncommutative field theory.

The recently observed by CLEO cascade decays ϒ(3S)→γχ'_bJ→γωϒ are discussed. It is shown that within the nonrelativistic description of bottomonium in the heavy b quark limit, the ratio of the rates of the transitions χ'_bJ→ωϒ with J = 1 and J = 2 should be given by the ratio of the corresponding S wave phase space factors. As a result, the rate of the observed cascade transitions through the χ'_b2 resonance should be close to that through the χ'_b1. It is suggested that the ratio of the discussed cascade rates can also be tested by measuring a simple angular correlation.