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

N=2 Super Yang Mills Action and BRST Cohomology

The extended BRST cohomology of N=2 super Yang-Mills theory is discussed in the framework of Algebraic Renormalization. In particular, N=2 supersymmetric descent equations are derived from the cohomological analysis of linearized Slavnov-Taylor operator \B. It is then shown that both off- and on-shell N=2 super Yang-Mills actions are related to a lower-dimensional gauge invariant field polynomial Tr\f^2 by solving these descent equations. Moreover, it is found that these off- and on-shell solutions differ only by a \B-exact term, which can be interprated as a consequence of the fact that the cohomology of both cases are the same.Comment: Latex, 1+13 page

Seeing the Invisible Axion in the Sparticle Spectrum

I describe how under favourable circumstances the invisible axion may manifest its existence at the LHC through the sparticle spectrum; in particular through a gluino \sim \ln (M_P/m_{3/2}) times heavier than other gauginos.Comment: 4 pages, REVTe

Two-Parameter Differential Calculus on the h-Exterior Plane

We construct a two-parameter covariant differential calculus on the quantum $h$-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.Comment: 7 page

Supersymmetric Canonical Commutation Relations

We present unitarily represented supersymmetric canonical commutation relations which are subsequently used to canonically quantize massive and massless chiral,antichiral and vector fields. The massless fields, especially the vector one, show new facets which do not appear in the non superymmetric case. Our tool is the supersymmetric positivity induced by the Hilbert-Krein structure of the superspace.Comment: 14 page

The Standard Model on Non-Commutative Space-Time

We consider the Standard Model on a non-commutative space and expand the action in the non-commutativity parameter theta. No new particles are introduced, the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard Model. At leading order in theta we find new vertices which are absent in the Standard Model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered.Comment: 28 pages, v3: typos corrected, new appendix on alternative kinetic terms for gauge bosons; v4: typos correcte

Effect of quantum fluctuations on topological excitations and central charge in supersymmetric theories

The effect of quantum fluctuations on Bogomol'nyi-Prasad-Sommerfield (BPS)-saturated topological excitations in supersymmetric theories is studied. Focus is placed on a sequence of topological excitations that derive from the same classical soliton or vortex in lower dimensions and it is shown that their quantum characteristics, such as the spectrum and profile, differ critically with the dimension of spacetime. In all the examples examined the supercharge algebra retains its classical form although short-wavelength fluctuations may modify the operator structure of the central charge, yielding an anomaly. The central charge, on taking the expectation value, is further affected by long-wavelength fluctuations, and this makes the BPS-excitation spectra only approximately calculable in some low-dimensional theories. In four dimensions, in contrast, holomorphy plays a special role in stabilizing the BPS-excitation spectra against quantum corrections. The basic tool in our study is the superfield supercurrent, from which the supercharge algebra with a central extension is extracted in a supersymmetric setting. A general method is developed to determine the associated superconformal anomaly by considering dilatation directly in superspace.Comment: 10 pages, Revtex, to appear in PR

The 'Square Root' of the Interacting Dirac Equation

The 'square root' of the interacting Dirac equation is constructed. The obtained equations lead to the Yang-Mills superfield with the appropriate equations of motion for the component fields.Comment: 6 page

Van der Waerden calculus with commuting spinor variables and the Hilbert-Krein structure of the superspace

Working with anticommuting Weyl(or Mayorana) spinors in the framework of the van der Waerden calculus is standard in supersymmetry. The natural frame for rigorous supersymmetric quantum field theory makes use of operator-valued superdistributions defined on supersymmetric test functions. In turn this makes necessary a van der Waerden calculus in which the Grassmann variables anticommute but the fermionic components are commutative instead of being anticommutative. We work out such a calculus in view of applications to the rigorous conceptual problems of the N=1 supersymmetric quantum field theory.Comment: 14 page