Off-shell Realization of Invariant Systems with special treatment of supersymmetric models
Off-shell Realization of Invariant Systems with special treatment of supersymmetric models
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Date
2013-12-08
Auteurs
Djeghloul Nazim
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Éditeur
Université Oran1 Ahmed Ben Bella
Résumé
This thesis is devoted to the construction of a general framework for the off-shell realization of (principally) irreducible invariant field theories plagued with an open algebra of symmetries, i.e., which closes up to the field equations of motion. After a brief review of classical features related to the implication of the symmetry algebra structure on the BRST construction at both on-shell and off-shell levels, we present a prescription that allows us to introduce the auxiliary fields structure for a given open gauge algebra leading to the desired off-shell realization. Global symmetries are also implemented as well as an outline concerning irreducible theories.
A central part of this work deals with applications to supersymmetric models. Standard “old minimal” auxiliary fields structure for D=4, N=1 supergravity is recovered and a new one is presented. For the latter we emphasize that the off-shell bosonic and fermionic degrees of freedom do not balance. This leads us to propose an amendment to the "bosons=fermions" rule in supersymmetry (at the off-shell level) and allows us to find a less restrictive condition.
Applications are also performed for N=1 global supersymmetry in the context of the Wess-Zumino model and for the extended N=2 case. We focus on two models of the extended N=2 supersymmetry. These models are the Fayet-Sohnius (N=2) supersymmetric matter model and the Double Tensor multiplet for which the off-shell construction usually fails. To find out the desired off-shell structure, we perform, in addition to the application of our procedure, a modification of the extended standard N=2 supersymmetry algebra in order to implement the symmetric group S₂, which describes also a discrete symmetry of the models under consideration.
Finally, we briefly discuss the case of reducible systems by taking advantage of the possibility of replacing a reducible gauge theory by an irreducible one, keeping the physical observables unchanged. We then give, accordingly to our off-shell realization procedure, the auxiliary fields structure for the irreducible version of the original reducible system.
Description
Mots-clés
BRST formalism,
Irreducible systems,
Auxiliary fields,
Open algebras,
Off-shell construction,
Extended N=2 supersymmetry, Supersymmetry, imple supergravity, Reducible theories,
Off-shell/On-shell gauge theories