Two-dimensional Superspace Research Articles

Ectoplasm and superspace integration measures for 2D supergravity with four spinorial supercurrents

Building on a previous derivation of the local chiral projector for a two-dimensional superspace with eight real supercharges, we provide the complete density projection formula required for locally supersymmetrical theories in this context. The derivation of this result is shown to be very efficient using techniques based on the ectoplasmic construction of local measures in superspace.

(2,0) Super-Beltrami parametrization and superconformal structures

The superconformal structure of the (2,0) supergeometry of two-dimensional superspace is characterized by the Beltrami differentials. The superdiffeomorphism transformations of the Beltrami variables are given and the superfields with arbitrary conformal weights are studied.

Left-right decomposition of two-dimensional superspace geometry and its BRS structure

Abstract Two-dimensional (1, 1) superspace geometry is reviewed with special emphasis on its Beltrami parametrization and the factorization of the corresponding BRS transformations. Generic matter superfields of arbitrary chiral weights are discussed in this geometrical setting. Based upon a thorough discussion of the purely bosonic case these supersymmetric structures are presented in superfield formalism as well as in component field language.

Left-right decomposition of two-dimensional superspace geometry and its BRS structure : R. Grimm. Institut für Theoretische Physik, Universität Karlsruhe, Kaiserstrasse 12, D-7500 Karlsruhe 1, Federal Republic of Germany

Left-right decomposition of two-dimensional superspace geometry and its BRS structure : R. Grimm. Institut für Theoretische Physik, Universität Karlsruhe, Kaiserstrasse 12, D-7500 Karlsruhe 1, Federal Republic of Germany

Factorization of the BRST algebra on superconformal structures

Abstract We introduce the superfield analog of the Beltrami differential. We characterize in this way the superconformal structure of the geometry of two-dimensional superspace. We obtain the superdiffeomorphism transformations of these fields under the form of a graded differential (BRST) algebra. The factorization of this algebra has an obvious interest in superstring theory. Superfields with arbitrary conformal weights are studied.

Supersymmetric Yang-Mills theory in two-dimensional superspace and super Kac-Moody algebra

Abstract We formulate N =1 supersymmetric Yang-Mills theory in two-dimensional superspace. In constructing the superspace formalism for the gauge theory we find that we should adopt unconventional constraints. It is shown that under these constraints the gauge symmetry derives a super Kac-Moody algebra.

Bosonic and spinning Weyl-invariant rigid strings

We present a number of new bosonic Weyl-invariant rigid strings. We also find world sheet supersymmetric and super Weyl-invariant counterparts to some of them, using two-dimensional superspace supergravity.

The Witten index in superspace, two-dimensional superanomaly in Yang-Mills and gravitational background, and superspace Schwinger-Dewitt heat kernel method

We consider the Witten index in superspace and show that it is closely related to the superspace Schwinger-DeWitt heat kernel. By evaluating the Witten index for the two-dimensional superspace Yang-Mills and gravitational systems we obtain the two-dimensional superanomaly in an efficient way. Furthermore we show an effective way to treat the three-dimensional supersymmetric Yang-Mills system by the superspace Schwinger-DeWitt heat kernel method. As a consequence, the supersymmetric Chern-Simons term is obtained.

Modulated Kronig-Penney model in superspace

The wave functions of electrons in a one-dimensional Kronig-Penney model with modulated positions of the delta-potentials are studied in a 2-dimensional space. The analytic behaviour of the density throws light on the character of the density function in one dimension because the latter is a section of the two-dimensional superspace. The model shows localized, extended and pseudolocalized states.

Superfield Approach to Systems of Two and Three Spinning Particles

Systems of two and three spinning particles are investigated by regarding each particle as a superfield defined in a two-dimensional superspace. It is shown that the resultant systems become respective bi-local counterparts of the Neveu-Schwarz model and the Ramond model in the dual model theory. Short comments on the massive particle and the interaction with an external gauge field are also given.

Supersymmetric actions for spinning particles

We review and investigate a number of supersymmetric actions describing a "classical particle of spin 1/2." The supersymmetry is introduced by extending the one-dimensional parameter space used to describe a conventional point particle to a two-dimensional superspace. The structure of this superspace is studied and a tensor calculus is developed. Different ways to modify the action of a conventional point particle to a superspace action are then considered. The superspace actions are simplified by a gauge choice and by elimination of some superfluous variables. Finally, the anticommuting parameter is eliminated, and the models are shown to be identical to models which have been studied earlier and shown to describe a "classical spin-1/2 particle". We take care to prove that the variable eliminations and gauge choices do not change the content of the models and to exhibit clearly the symmetries at each stage.