Perturbative Gravity in the Causal Approach

Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory. We prove gauge invariance and renormalizability in the second order of perturbation theory for the pure gravity system (massless and massive). Then we investigate the interaction of massless gravity with matter (described by scalars and spinors) and massless Yang-Mills fields. We obtain a difference with respect to the classical field theory due to the fact that in quantum field theory one cannot enforce the divergenceless property on the vector potential and this spoils the divergenceless property of the usual energy-momentum tensor. To correct this one needs a supplementary ghost term in the interaction Lagrangian.Comment: 50 pages, no figures, some changes in the last sectio

(4,4) superfield supergravity

We present the N=4 superspace constraints for the two-dimensional (2d) off-shell (4,4) supergravity with the superfield strengths expressed in terms of a (4,4) twisted (scalar) multiplet TM-I, as well as the corresponding component results, in a form suitable for applications. The constraints are shown to be invariant under the N=4 super-Weyl transformations, whose N=4 superfield parameters form another twisted (scalar) multiplet TM-II. To solve the constraints, we propose the Ansatz which makes the N=4 superconformal flatness of the N=4 supergravity curved superspace manifest. The locally (4,4) supersymmetric TM-I matter couplings, with the potential terms resulting from spontaneous supersymmetry breaking, are constructed. We also find the full (4,4) superconformally invariant (improved) TM-II matter action. The latter can be extended to the (4,4) locally supersymmetric Liouville action which is suitable for describing (4,4) supersymmetric non-critical strings.Comment: 32 pages, LaTeX, revised version (one reference added, and one Appendix is reduced

Gauge theory in deformed N=(1,1) superspace

We review the non-anticommutative Q-deformations of N=(1,1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) Spin(4) ``Lorentz'' symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed N=(1,0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the abelian case. For the charged hypermultiplet in an abelian gauge superfield background we construct the deformed holomorphic effective action.Comment: 1+60 pages, typos corrected, references adde

Mass predictions based on a supersymmetric SU(5) fixed point

I examine the possibility that the third generation fermion masses are determined by an exact fixed point of the minimal supersymmetric SU(5) model. When one-loop supersymmetric thresholds are included, this unified fixed point successfully predicts the top quark mass, 175 +(-) 2 GeV, as well as the weak mixing angle. The bottom quark mass prediction is sensitive to the supersymmetric thresholds; it approaches the measured value for mu <0 and very large unified gaugino mass. The experimental measurement of the tau lepton mass determines tan(beta), and the strong gauge coupling and fine structure constant fix the unification scale and the unified gauge coupling.Comment: 40 pages, 9 figures, 9 tables, Revtex

Unfolded Scalar Supermultiplet

Unfolded equations of motion for N = 1, D = 4 scalar supermultiplet are presented. We show how the superspace formulation emerges from the unfolded formulation. To analyze supersymmetric unfolded equations we extend the \sigma_-cohomology technics to the case with several operators \sigma_. The role of higher \sigma_-cohomology in the derivation of constraints is emphasized and illustrated by the example of scalar supermultiplet.Comment: 27 pages, no figures; minor corrections: clarifications added, typos correcte

Correlation Functions of Conserved Currents in N = 2 Superconformal Theory

Using a manifestly supersymmetric formalism, we determine the general structure of two- and three- point functions of the supercurrent and the flavour current of N = 2 superconformal field theories. We also express them in terms of N = 1 superfields and compare to the generic N = 1 correlation functions. A general discussion of the N = 2 supercurrent superfield and the multiplet of anomalies and their definition as derivatives with respect to the supergravity prepotentials is also included.Comment: 43 pages, latex, no figures, v.2: section 4.2 extende