Noncommutative Supersymmetry in Two Dimensions

Abstract

Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the $\mathcal{N}=1$ super $E^2$ algebra associated to the deformation of translations in a noncommutative Euclidean plane. The algebra is obtained using appropriate representaions of its generators on the space of superfields in a $D=2,\mathcal{N}=1$ ``noncommutative superspace.'' We find that the (anti)commutators between several (super)translation generators are no longer vanishing, but involve a new set of generators which together with the (super)translation and rotation generators form a consistent closed algebra. We then analyze the spectrum of this algebra in order to obtain its fundamental and adjoint representations.

30 pages, Latex, no figures, some modifications including change of notations and addition of some comments

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Cited by in corpus (5)

• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Ring Structure of SUSY * Product and 1/2 SUSY Wess-Zumino Model
• Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States
• Scalar Solitons in Non(anti)commutative Superspace
• Recovery of Full N=1 Supersymmetry in Non(anti-)commutative Superspace