Reality in Noncommutative Gravity

We study the problem of reality in the geometric formalism of the 4D noncommutative gravity using the known deformation of the diffeomorphism group induced by the twist operator with the constant deformation parameters \vt^{mn}. It is shown that real covariant derivatives can be constructed via $\star$-anticommutators of the real connection with the corresponding fields. The minimal noncommutative generalization of the real Riemann tensor contains only \vt^{mn}-corrections of the even degrees in comparison with the undeformed tensor. The gauge field $h_{mn}$ describes a gravitational field on the flat background. All geometric objects are constructed as the perturbation series using $\star$-polynomial decomposition in terms of $h_{mn}$. We consider the nonminimal tensor and scalar functions of $h_{mn}$ of the odd degrees in \vt^{mn} and remark that these pure noncommutative objects can be used in the noncommutative gravity.Comment: Latex file, 14 pages, corrected version to be publised in CQ

(Non)renormalizability of the D-deformed Wess-Zumino model

We continue the analysis of the $D$-deformed Wess-Zumino model which was started in the previous paper. The model is defined by a deformation which is non-hermitian and given in terms of the covariant derivatives $D_\alpha$. We calculate one-loop divergences in the two-point, three-point and four-point Green functions. We find that the divergences in the four-point function cannot be absorbed and thus our model is not renormalizable. We discuss possibilities to render the model renormalizable.Comment: 19 pages; version accepted for publication in Phys.Rev.D; new section with the detailed discussion on renormalizabilty added and a special choice of coupling constants which renders the model renormalizable analyze

Sparticle Mass Spectrum in Grand Unified Theories

We carry out a detailed analysis of sparticle mass spectrum in supersymmetric grand unified theories. We consider the spectroscopy of the squarks and sleptons in SU(5) and SO(10) grand unified theories, and show how the underlying supersymmetry breaking parameters of these theories can be determined from a measurement of different sparticle masses. This analysis is done analytically by integrating the one-loop renormalization group equations with appropriate boundary conditions implied by the underlying grand unified gauge group. We also consider the impact of non-universal gaugino masses on the sparticle spectrum, especially the neutralino and chargino masses which arise in supersymmetric grand unified theories with non-minimal gauge kinetic function. In particular, we study the interrelationships between the squark and slepton masses which arise in grand unified theories at the one-loop level, which can be used to distinguish between the different underlying gauge groups and their breaking pattern to the Standard Model gauge group. We also comment on the corrections that can affect these one-loop results.Comment: 19 pages, 6 figure

Non(anti)commutative superspace with coordinate-dependent deformation

We consider non(anti)commutative superspace with coordinate dependent deformation parameters $C^{\alpha\beta}$. We show that a chiral ${\cal N}=1/2$ supersymmetry can be defined and that chiral and antichiral superfields are still closed under the Moyal-Weyl associative product implementing the deformation. A consistent ${\cal N}=1/2$ Super Yang-Mills deformed theory can be constructed provided $C^{\alpha\beta}$ satisfies a suitable condition which can be connected with the graviphoton background at the origin of the deformation. After adding matter we also discuss the Konishi anomaly and the gluino condensation.Comment: References added. Accepted for publication in PR

Supergravity and IOSp(3,1|4) gauge theory

A new formulation of simple D=4 supergravity in terms of the geometry of superspace is presented. The formulation is derived from the gauge theory of the inhomogeneous orthosymplectic group IOSp(3,1|4) on a (4,4)-dimensional base supermanifold by imposing constraints and taking a limit. Both the constraints and the limiting procedure have a clear {\it a priori} physical motivation, arising from the relationship between IOSp(3,1|4) and the super Poincar\'{e} group. The construction has similarities with the space-time formulation of Newtonian gravity.Comment: 17 pages. Expanded version. To appear in Class. Quantum Gra

Topological Defects in Twisted Bundles of Two-Dimensionally Ordered Filaments

Twisted assemblies of filaments in ropes, cables and bundles are essential structural elements in wide use in macroscopic materials as well as within the cells and tissues of living organisms. We develop the unique, non-linear elastic properties of twisted filament bundles that derive from generic properties of two-dimensional line-ordered materials. Continuum elasticity reveals a formal equivalence between the elastic stresses induced by bundle twist and those induced by the positive curvature in thin, elastic sheets. These geometrically-induced stresses can be screened by 5-fold disclination defects in lattice packing, and we predict a discrete spectrum elastic energy groundstates associated with integer numbers of disclinations in cylindrical bundles. Finally, we show that elastic-energy groundstates are extremely sensitive to defect position in the cross-section, with off-center disclinations driving the entire bundle to buckle, adopting globally writhing configurations.Comment: 4.1 pages; 3 figure

Comment on triple gauge boson interactions in the non-commutative electroweak sector

In this comment we present an analysis of electroweak neutral triple gauge boson couplings projected out of the gauge sector of the extended non-commutative standard model. A brief overview of the current experimental situation is given.Comment: 4 page

Exact low-energy effective actions for hypermultiplets in four dimensions

We consider the general hypermultiplet Low-Energy Effective Action (LEEA) that may appear in quantized, four-dimensional, N=2 supersymmetric, gauge theories, e.g. in the Coulomb and Higgs branches. Our main purpose is a description of the exact LEEA of n magnetically charged hypermultiplets. The hypermultiplet LEEA is given by the N=2 supersymmetric Non-Linear Sigma-Model (NLSM) with a 4n-dimensional hyper-K"ahler metric, subject to non-anomalous symmetries. Harmonic Superspace (HSS) and the NLSM isometries are very useful to constrain the hyper-K"ahler geometry of the LEEA. We use N=2 supersymmetric projections of HSS superfields to N=2 linear (tensor) O(2) and O(4) multiplets in N=2 Projective Superspace (PSS) to deduce the explicit form of the LEEA in some particular cases. As the by-product, a simple new classification of all multi-monopole moduli space metrics having su(2)_R symmetry is proposed in terms of real quartic polynomials of 2n variables, modulo Sp(n) transformations. The 4d hypermultiplet LEEA for n=2 can be encoded in terms of an elliptic curve.Comment: 60 pages, LaTeX, macros included, references adde

The photon-neutrino interaction in non-commutative gauge field theory and astrophysical bounds

In this letter we propose a mechanism of left- and right-handed neutrino couplings to photons, which arises naturally in non-commutative gauge field theory. We estimate the predicted additional energy-loss in stars induced by space-time non-commutativity. The usual requirement that any new energy-loss mechanism in globular cluster stars must not significantly exceed the standard neutrino losses implies a scale of non-commutative gauge theory above the scale of weak interactions