A Path Integral Approach To Noncommutative Superspace

Abstract

A path integral formula for the associative star-product of two superfields is proposed. It is a generalization of the Kontsevich-Cattaneo-Felder's formula for the star-product of functions of bosonic coordinates. The associativity of the star-product imposes certain conditions on the background of our sigma model. For generic background the action is not supersymmetric. The supersymmetry invariance of the action constrains the background and leads to a simple formula for the star-product.

Latex 13 pages. v2: references and footnotes added

References in corpus (6)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• A path integral approach to the Kontsevich quantization formula
• Non(anti)commutative Superspace
• Covariant Quantization of the Green-Schwarz Superstring in a Calabi-Yau Background
• The Covariant Quantum Superstring and Superparticle from their Classical Actions
• Quantum Deformation of the Poincare Supergroup and $\kappa$-deformed Superspace

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• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Comments on Noncommutative Superspace
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• Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings
• Gauge Theory on Noncommutative Supersphere from Supermatrix Model
• D=2, N=2, Supersymmetric theories on Non(anti)commutative Superspace
• Superfield theory and supermatrix model
• Superstar in Noncommutative Superspace via Covariant Quantization of the Superparticle
• Ring Structure of SUSY * Product and 1/2 SUSY Wess-Zumino Model
• Recovery of Full N=1 Supersymmetry in Non(anti-)commutative Superspace
• The standard electroweak model in the noncommutative $DFR$ space-time
• Non-topological non-commutativity in string theory
• Supersymmetric Poisson and Poisson-supersymmetric sigma models