Scalar Solitons in Non(anti)commutative Superspace

Abstract

We study solitonic solutions of a deformed Wess-Zumino model in 2 dimensions, corresponding to a deformation of the usual $\mathcal{N}=1,D=2$ superspace to the one with non-anticommuting odd supercoordinates. The deformation turns out to add a kinetic term for the auxiliary field besides the known $F^3$ term coming from the deformation of the cubic superpotential. Both these modifications are proportional to the effective deformation parameter $\lambda \equiv \det C$, where $C$ denotes the non-anticommutativity matrix. We find a modified ``orbit'' equation which on the EOM relates the auxiliary and the scalar components of the scalar superfield as a first order correction to the usual relation in terms of the small parameter $\lambda$. Subsequently, we obtain the modified form of the first order BPS equation for the scalar field and find its solution to first order in $\lambda$. Issues such as modification of the BPS mass formula and a non-linear realization of the $\mathcal{N}=1$ supersymmetry are discussed.

25 pages, Latex file, 2 eps figures

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• Noncommutative Field Theory
• Noncommutative Solitons
• A Perturbative Window into Non-Perturbative Physics
• Non-commutative superspace from string theory
• Non(anti)commutative Superspace
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• Two-loop Renormalization for Nonanticommutative N=1/2 Supersymmetric WZ Model
• Renormalizability of N=1/2 Wess-Zumino model in superspace
• Deformed N=1 supersymmetry
• Generalized Noncommutative Supersymmetry from a New Gauge Symmetry
• Spacetime Supersymmetry in a nontrivial NS-NS Superstring Background
• Noncommutative Supersymmetry in Two Dimensions

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• Comments on Gluino Condensates in N=1/2 SYM Theory
• Gauge Theory on Noncommutative Supersphere from Supermatrix Model
• Gauged Wess-Zumino Model in Noncommutative Minkowski Superspace
• N=1/2 Super Yang-Mills Theory on Euclidean AdS2xS2
• Seiberg-Witten Map for Superfields on N=(1/2,0) and N=(1/2,1/2) Deformed Superspace
• Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States