21-26 July 2014
Renold Building
Europe/London timezone
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Deformation in SUSY 2+1

Presented by Mr. Carlos IPIA on 24 Jul 2014 from 14:50 to 15:10
Type: Formal SUSY and Strings
Track: Formal SUSY and Strings


The non-commutativity of space-time has been proposed as an attempt to incorporate in quantum mechanics and quantum field theory some properties that should be part of a consistent quantum theory of gravitation. A non-trivial aspect of this type of proposal is the fate of spacetime symmetries in this context. Some of the most popular versions for non-commutative spaces explicitly violate Lorentz invariance. A proposal to implement non-commutativity in space-time preserving, somehow, the notion of relativistic invariance involves the use of Hopf algebras as "deformations" of the Poincaré algebra, via the so-called Drinfel'd twist. In this paper, we study the application of the Drinfel'd twist to supersymmetric theories. It is shown that the main properties of a superalgebra can be rewritten using the language of Hopf algebras, and so we can apply the concept of twist deformation to the supersymmetric algebra of generators and superfields. After reviewing some existing approaches in the literature on non commutativity in superspace, we focus our study in the case of three-dimensional space-time. Using the formalism of Hopf algebras, we introduce the non anticomutativity to the Grassmanian superspace coordinates,and describe the corresponding deformed superalgebra, defining new supersymmetry generators that satisfy the usual supersymmetric algebra. Finally, we constructed an action invariant under this deformed algebra, and concluded that the terms that bear the modifications arising from the non anticomutativity of coordinates are the interaction terms,while the quadratic part of the action is not modified.


Location: Renold
Room: E1

Primary authors