THE NONCOMMUTATIVE SUPERSYMMETRIC NONLINEAR SIGMA MODEL

We show that the noncommutativity of space–time destroys the renormalizability of the 1/N expansion of the O(N) Gross–Neveu model. A similar statement holds for the noncommutative nonlinear sigma model. However, we show that, up to the subleading order in 1/N expansion, the noncommutative supersymmetric O(N) nonlinear sigma model becomes renormalizable in D=3. We also show that dynamical mass generation is restored and there is no catastrophic UV/IR mixing. Unlike the commutative case, we find that the Lagrange multiplier fields, which enforce the supersymmetric constraints, are also renormalized. For D=2 the divergence of the four-point function of the basic scalar field, which in D=3 is absent, cannot be eliminated by means of a counterterm having the structure of a Moyal product.

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 nonlinear sigma-model (NLSM) with a 4n-dimensional hyper-Kähler metric, subject to nonanomalous symmetries. Harmonic superspace (HSS) and the NLSM isometries are very useful to constrain the hyper-Kähler 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=2projective superspace (PSS) to deduce the explicit form of the LEEA in some particular cases. As the by-product, a simple new classification of all multimonopole 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.

THE NEUTRALINO SECTOR IN STRONGLY INTERACTING SUPERSYMMETRIC MODELS

The neutralino sector is analyzed for a supersymmetric nonlinear sigma model. This model describes the low energy physics of strongly interacting theories in which super-symmetry is softly broken at scales below the electroweak symmetry breaking scale. The measured width of the Z boson constrains the allowed range of parameters. In case the lightest neutralino is stable, limits on additional contributions to the invisible width of the Z boson and on the relic neutralino density further restrict parameter space. As a consequence, the lightest neutralino in the considered class of theories is required to have a mass above 15 GeV, but below MZ.

SYMPLECTIC QUANTIZATION OF SUPERFIELDS

We show how the extension of the Faddeev-Jackiw symplectic quantization (including true constraints) can be used in superspace. We first deal with supersymmetric free field theory in the component language. After that, we consider the method applied to superfields, taken as canonical variables. We also use the formalism, directly in superfield formulation, for the supersymmetric nonlinear sigma model.

ON THE QUANTIZATION OF THE N = 2 SUPERSYMMETRIC NONLINEAR SIGMA MODEL

A method for quantizing the bidimensional N = 2 supersymmetric nonlinear sigma model is developed. This method is both covariant under coordinate transformations (concerning the order relevant for calculation) and explicitly N = 2 supersymmetric. The operator product expansion of the supercurrent is computed accordingly, including also the dilaton. By imposing the N = 2 superconformal algebra the equations for the metric and the dilaton are obtained. In particular, they imply that the dilaton is a constant.