A systematic algorithm to derive superpropagators in the case of either explicitly or spontaneously broken supersymmetric three-dimensional theories is presented. We discuss how the explicit breaking terms that are introduced at tree-level induce 1-loop radiative corrections to the effective action. We also point out that the renormalisation effects and the breaking-inducing-breaking mechanism become more immediate whenever we adopt the shifted superpropagators discussed in this letter.Comment: 6 pages, LaTex, references added. To appear in Phys.Lett.

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In this letter, we present the Parkes-Siegel formulation for the massive Abelian N =1 super-QED 2+2 coupled to a self-dual supermultiplet, by introducing a chiral multiplier superfield. We show that after carrying out a suitable dimensional reduction from (2+2) to (1+2) dimensions, and performing some necessary truncations, the simple supersymmetric extension of the τ 3 QED 1+2 coupled to a Chern-Simons term naturally comes out.The issue of self-duality has deserved a great deal of attention since a self-dual Yang-Mills theory in Atiyah-Ward space-time (2+2 dimensions) [1] has been pointed out as a source for various integrable models in lower dimensions, according to a conjecture by Atiyah and Ward [2].Recently, the simple supersymmetric version of the self-dual Yang-Mills theory and selfdual supergravity model in Atiyah-Ward space-time has been formulated by Gates, Ketov and Nishino [3]. Also, by a suitable dimensional reduction proposed by Nishino, N=1 and N=2 super-Chern-Simons theories in D=1+2 were generated from N=1 and N=2 super-self-dual Yang-Mills theories in D=2+2 [4].In the last years, 3-dimensional field theories [5] have been well-motivated in view of the possibilities of providing a gauge-theoretical foundation for the description of condensed matter phenomena, such as high-T c superconductivity [6], where the QED 3 and τ 3 QED 1+2 [6,7] are some of the theoretical approaches used to understand more deeply about high-T c materials. The finiteness on the Landau gauge of Chern-Simons theories [8] is also an interesting result that motivates the study of 3-dimensional gauge theories.The relationship between massive Abelian N=1 super-QED 2+2 in Atiyah-Ward space-time and N=1 super-τ 3 QED in D=1+2 has already been investigated by carrying out a dimensional reductionà la Scherk from (2+2) to (1+2) dimensions and by performing some suitable supersymmetry-preserving truncations [9,10]. * On leave of absence from the Brazilian

Clifford algebras and Majorana conditions are analyzed in any spacetime. An index labeling inequivalent Γ-structures up to orthogonal conjugations is introduced.Inequivalent charge-operators in even-dimensions, invariant under Wick rotations, are considered. The hermiticity condition on free-spinors lagrangians is presented. The constraints put by the Majorana condition on the free-spinors dynamics are analyzed. Tables specifying which spacetimes admit lagrangians with non-vanishing kinetic, massive or pseudomassive terms (for both charge-operators in even dimensions) are given. The admissible free lagrangians for free Majorana-Weyl spinors are fully classified.April 1999 CBPF-NF-013/99 hep-th/xxx E-Mail: 1) marco@cat.cbpf.br 2) toppan@cat.cbpf.br

Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin(8) triality automorphisms. Different signature versions of theories such as 10-dimensional SYM's, superstrings, five-branes, F-theory, are shown to be interconnected via the S 3 permutation group. Bilinear and trilinear invariants under space-time triality are introduced and their possible relevance in building models possessing a space-versus-time exchange symmetry is discussed. Moreover the Cartan's "vector/chiral spinor/antichiral spinor" triality of SO(8) and SO(4, 4) is analyzed in detail and explicit formulas are produced in a Majorana-Weyl basis. This paper is the extended version of hep-th/9907148. CBPF-NF-009/00hep-th/xxx E-Mails: 1) marco@cbpf.br 2) mrojas@cbpf.br 3) toppan@cbpf.br

The basic arguments underlying the symplectic projector method are presented. By this method, local free coordinates on the constraint surface can be obtained for a broader class of constrained systems. Some interesting examples are analyzed. *

Spinors for an arbitrary Minkowski space with signature (t, s) are reassessed in connection with D-dimensional free Dirac action. The possibility of writing down kinetic and mass terms for charge-conjugated spinors is discussed in terms of the number of time-like directions of the space-time. The results found out here are commented in the light of early works on the subject. * Internet

We analyse the renormalizability of an Abelian N =1 super-Chern-Simons model coupled to paritypreserving matter on the light of the regularization independent algebraic method. The model shows to be stable under radiative corrections and to be gauge anomaly free.