Non(anti)commutative Superspace

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  • 23 April 2001
Abstract
We investigate the most general non(anti)commutative geometry in N=1 four dimensional superspace. We find that a nontrivial non(anti)commutative superspace geometry compatible with supertranslations exists with non(anti)commutation parameters which may depend on the spinorial coordinates. The algebra is in general nonassociative. Imposing associativity introduces additional constraints which however allow for nontrivial commutation relations involving fermionic coordinates. We define an associative *-product by extending to superspace the Kontsevich procedure. In a string theory contest we discuss the connection between non(anti)commutative grassmannian geometry in superspace and string propagation in curved backgrounds. Finally, N=2 euclidean superspace is also discussed.

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