On nonanticommutative N=2 sigma-models in two dimensions

Abstract

We study nonanticommutative deformations of N=2 two-dimensional Euclidean sigma models. We find that these theories are described by simple deformations of Zumino's Lagrangian and the holomorphic superpotential. Geometrically, this deformation can be interpreted as a fuzziness in target space controlled by the vacuum expectation value of the auxiliary field. In the case of nonanticommutative deformations preserving Euclidean invariance, we find that a continuation of the deformed supersymmetry algebra to Lorentzian signature leads to a rather intriguing central extension of the ordinary (2,2) superalgebra.

29 pages. Typos corrected and references added

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• Quantum Field Theory on Noncommutative Spaces
• Non-commutative superspace from string theory
• Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory
• Non(anti)commutative Superspace
• Some Aspects of Deformations of Supersymmetric Field Theories
• Phase structure of non-commutative scalar field theories
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• Supersymmetry in noncommutative superspaces
• Renormalizability of N=1/2 Wess-Zumino model in superspace
• Nilpotent deformations of N=2 superspace
• Renormalizability of Non(anti)commutative Gauge Theories with N=1/2 Supersymmetry
• Non-anticommutative N=2 super-Yang-Mills theory with singlet deformation
• Wilsonian Proof for Renormalizability of N=1/2 Supersymmetric Field Theories
• Non(anti)commutative Superspace, UV/IR Mixing & Open Wilson Lines
• Non-anticommutative chiral singlet deformation of N=(1,1) gauge theory
• N=1/2 gauge theory and its instanton moduli space from open strings in R-R background
• One-Loop Perturbative Corrections to non(anti)commutativity Parameter of N=1/2 Supersymmetric U(N) Gauge Theory
• One-loop renormalisation of N=1/2 supersymmetric gauge theory
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• D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace
• D=2, N=2 Supersymmetric sigma models on Non(anti)commutative Superspace
• Non-Anti-Commutative deformation of effective potentials in supersymmetric gauge theories
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• Chiral effective potential in $\mathcal{N}=1/2$ non-commutative Wess-Zumino model
• Deformed Supersymmetry in Non(anti)commutative N=2 Supersymmetric U(1) Gauge Theory
• Field Theory in Noncommutative Minkowski Superspace
• Generic chiral superfield model on nonanticommutative N=1/2 superspace
• Deformed N=1 supersymmetry
• Non-anticommutative N=2 supersymmetric SU(2) gauge theory
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Cited by in corpus (24)

• Supersymmetry vs ghosts
• Non-anticommutativity in Presence of a Boundary
• On quantum properties of the four-dimensional generic chiral superfield model
• Non-singlet Q-deformation of the N=(1,1) gauge multiplet in harmonic superspace
• Non(anti)commutative N=(1,1/2) Supersymmetric U(1) Gauge Theory
• Quantum Corrections in 2D SUSY CP^{N-1} Sigma Model on Noncommutative Superspace
• Cryptoreality of nonanticommutative Hamiltonians
• Construction of the effective action in nonanticommutative supersymmetric field theories
• Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States
• The non-anticommutative supersymmetric Wess-Zumino model
• Chiral Models in Noncommutative N=1/2 Four Dimensional Superspace
• Konishi Anomaly and Central Extension in N=1/2 Supersymmetry
• N=1/2 supersymmetric four-dimensional non-linear sigma-models from non-anti-commutative superspace
• The non-anticommutative supersymmetric U(1) gauge theory
• One-loop effective potential in $\mathcal{N}=1/2$ generic chiral superfield model
• Twist Deformations of the Supersymmetric Quantum Mechanics
• One-loop divergences in the two-dimensional non-anticommutative supersymmetric sigma-model
• Supersymmetric Nambu$-$Jona-Lasinio Model on $\mathcal{N}=1/2$ four-dimensional Non(anti)commutative Superspace
• Quantum Mechanics in Non(Anti)Commutative Superspace
• Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability
• A renormalisable non-anticommutative SU(N)xU(1) gauge theory in components
• Non-anticommutative solitons
• Central Charges in Non(anti)commutative N=2 Supersymmetric U(N) Gauge Theory
• Renormalisation of the non-anticommutativity parameter at two loops