Supersymmetric models on AdS3 and AdS4 embedding superspaces

Superspace techniques are used to formulate a supersymmetric model on an AdS3 surface embedded in four dimensions. In this model, the supersymmetry transformation is the “square root” of the transformation generated by the isometry generators of AdS3. Because momentum is not an isometry generator, supersymmetry does not result in equal masses for a bosonic field and its fermionic partner. We express this model in terms of coordinates that characterize the AdS3 space. In one coordinate system, it is possible to define a subspace with a Minkowski metric. It becomes possible to infer a model in AdS4 space in which there is a symmetry transformation that relates bosonic and fermionic fields. This model is not a consequence of being formulated in a superspace and the fermionic symmetry transformation is not the “square root” of an isometry of AdS4.

Generators of local supersymmetry transformation from first-class constraints

We show how the generator of local supersymmetry transformations can be found from fermionic first-class constraints. This is done by adapting the approaches of Henneaux, Teitelboim and Zanelli, and of Castellani that have been used to find the generator of gauge transformations from bosonic first-class constraints. We illustrate how a supersymmetric gauge generator can be found by considering a spinning particle. The invariances that we find are not those presented in the original discussion of the spinning particle.

GEOMETRIC IIA SUPERGRAVITY THEORIES IN THE STRING FRAME

Using the geometric (rheonomic) approach based on the Free Differential Algebra, we derive the full type IIA D = 10 supergravity Lagrangian in the string frame, including the Romans' mass deformation, and containing the explicit four-fermion interactions, absent from the original Romans' paper. This provides a deeper insight into the group theoretical and algebraic structures of the theory. Moreover we provide the full set of supersymmetry transformation laws both in the Romans'-deformed and undeformed theories. The structure of the bosonic Free Differential Algebra for the HLW deformation is also presented.

DEFORMATION OF SCHILD STRING

We attempt to construct new superstring actions with a D-plet of Majorana fermions [Formula: see text], where ℬ is the D-dimensional space–time index and A is the two-dimensional spinor index, by deforming the Schild action. As a result, we propose three kinds of actions: the first is invariant under N=1 (the worldsheet) supersymmetry transformation and the area-preserving diffeomorphism. The second contains the Yukawa type interaction. The last possesses some nonlocality because of bilinear terms of [Formula: see text]. The reasons why completing a Schild type superstring action with [Formula: see text] is difficult are finally discussed.

N=2 SUPERMULTIPLET OF CURRENTS AND ANOMALOUS TRANSFORMATIONS IN SUPERSYMMETRIC GAUGE THEORY

We examine some properties of supermultiplet consisting of the U (1)J current, extended supercurrents, energy–momentum tensor and the central charge in N = 2 supersymmetric Yang–Mills theory. The superconformal improvement requires adding another supermultiplet starting from the U (1)R current. We determine the anomalous (quantum mechanical) supersymmetry transformation associated with the central charge and the energy–momentum tensor to one-loop order. We find nonvanishing fermionic contribution to the central charge.

Quantum corrections to the supersymmetry algebra

The Bjorken–Johnson–Low technique is used to compute the equal time anticommutator of the spinor currents associated with the supersymmetry of a two-dimensional Wess–Zumino model containing a Majorana spinor, a scalar, and an auxiliary field. Operator regularization is used to compute radiative effects as this does not explicitly break the supersymmetry present in the classical Lagrangian. We find that the spinor current is not conserved, and that the algebra of the generators of the supersymmetry transformation is altered. This is analogous to what has been found in theories with a classical axial gauge symmetry.

D=10 SUPERSPACE GEOMETRY AND HETEROTIC SUPERSTRING THEORY (I)

Using a Weyl transformation in superspace, we provide a noncanonical formulation of standard D=10, N=1 supergravity, including the gauge matter sector. This formulation turns out to be ideally suited for carrying out the renormalization of the Green-Schwarz σ-model describing the D=10 heterotic string propagating in a curved background space. By reducing the superspace results to the component level, we derive the supersymmetry transformation laws for the component fields of the theory.