International Journal of Modern Physics A

We consider various modifications of the Weyl–Moyal star-product, in order to obtain a finite range of nonlocality. The basic requirements are to preserve the commutation relations of the coordinates as well as the associativity of the new product. We show that a modification of the differential representation of the Weyl–Moyal star-product by an exponential function of derivatives will not lead to a finite range of nonlocality. We also modify the integral kernel of the star-product introducing a Gaussian damping, but find a nonassociative product which remains infinitely nonlocal. We are therefore led to propose that the Weyl–Moyal product should be modified by a cutoff-like function, in order to remove the infinite nonlocality of the product. We provide such a product, but it appears that one has to abandon the possibility of analytic calculation with the new product.

Supposing quark–diquark structure of baryons, we look for systematics of baryons composed of light quarks (q = u, d). We systematize baryons using the notion of two diquarks: (i) axial–vector state, , with the spin S_D = 1 and isospin I_D = 1 and (ii) scalar one, , with the spin S_D = 0 and isospin I_D = 0. We consider several schemes for the composed baryons: (1) with different diquark masses, , (2) with and overlapping and states (resonances), (3) with/without SU(6) constraints for low-lying states (with quark–diquark orbital momenta L = 0). In the high-mass region, the model predicts several baryon resonances at M ~ 2.0–2.9 GeV. Moreover, the model gives us the double pole structure (i.e. two poles with the same Re M but different Im M) in many amplitudes at masses M ≳ 2.0 GeV. We see also that for description of low-lying baryons (with L = 0), the SU(6) constraint is needed.

We study the pseudoduality transformation in supersymmetric sigma models. We generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold and by orthonormal coframe method on manifold . The component expansion method yields the result that pseudoduality tranformation is not invertible at all points and occurs from all points on one manifold to only one point where Riemann normal coordinates are valid on the second manifold. Torsion of the sigma model on must vanish while it is nonvanishing on , and curvatures of the manifolds must be constant and the same. In the case of super-WZW sigma models, pseudoduality equations result in three different pseudoduality conditions; identity, chiral and antichiral pseudoduality.

The most general SU(3)-singlet space of gauged supergravity in four-dimensions is studied recently. The SU(3)-invariant six scalar fields are realized by six real four-forms. A family of holographic supersymmetric RG flows on M2-branes in three-dimensions is described. This family of flows is driven by three independent mass parameters from the theory and is controlled by two IR fixed points, -invariant one and -invariant one. The generic flow with arbitrary mass parameters is supersymmetric and reaches to the fixed point where the three masses become identical. A particular supersymmetric SU(3)-preserving RG flow from the -invariant fixed point to the -invariant fixed point is also discussed.

Bianchi type-I string cosmological models with time dependent gauge function (β) within the framework of Lyra geometry is presented. To get the deterministic model of the universe, we assume that the eigenvalue of shear tensor is proportional to the expansion (θ). This leads to A = (BC)ⁿ where A, B, C are metric potential and n is a constant. The physical and geometrical aspects of the model are discussed in detail. In a special case, the behavior of the model in terms of cosmic time t for is also discussed.

Generalized Kerr–NUT–de Sitter space–time is the most general space–time which admits a rank-2 closed conformal Killing–Yano tensor. It contains the higher-dimensional Kerr–de Sitter black holes with partially equal angular momenta. We study the separability of gravitational perturbations in the generalized Kerr–NUT–de Sitter space–time. We show that a certain type of tensor perturbations admits the separation of variables. The linearized perturbation equations for the Einstein condition are transformed into the ordinary differential equations of Fuchs type.

In the last years, the idea of the existence of a collapsing phase previous to the actual expanding one has attracted attention in many different contexts (being very active!). There are many reasons for this, which concerns the standard model and its difficulties in dealing with a singularity which — in the words of the creator of general relativity — means the failure of the equations of general relativity to represent the gravitational field in those regions of extraordinary high curvature. However, we would like to point out just one: the possibility of deciding the existence of such primordial collapsing phase by observational tests due to the inprint it could be left in the inhomogeneous structure that constitutes the actual distribution of galaxies and cluster of galaxies. In this vein, the purpose of the present work is to analyze a particular bouncing universe and the evolution of small perturbations. To realize such analysis when the geometry has a bouncing (that is, the associated Hubble parameter — that measures the rate of the velocity of the expansion through — has a zero) the standard Lifshitz–Bardeen–Mukhanov variables/method is not the best one. Instead, we use the most well-behaved standard quasi-Maxwellian equations of perturbation introduced by Hawking and developed by Ellis et al. and Novello et al.

We use the global embedding Minkowski space geometries of a (3+1)-dimensional curved Reissner–Nordström (RN)–AdS black hole space–time into a (5+2)-dimensional flat space–time to define a proper local temperature, which remains finite at the event horizon, for freely falling observers outside a static black hole. Our extended results include the known limiting cases of the RN, Schwarzschild–AdS and Schwarzschild black holes.