Noncommutative Superspace, Supermatrix and Lowest Landau Level

Details Noncommutative Superspace, Supermatrix and Lowest Landau Level Noncommutative Superspace, Supermatrix and Lowest Landau Level

2003-06-25

arxiv.org/abs/hep-th/0306251v2

Nucl.Phys. B671 (2003) 217-242

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, Latex. A subsection is added to explain the Seiberg's noncommutative superspace as a constrained system

Scientific paper

By using graded (super) Lie algebras, we can construct noncommutative superspace on curved homogeneous manifolds. In this paper, we take a flat limit to obtain flat noncommutative superspace. We particularly consider $d=2$ and $d=4$ superspaces based on the graded Lie algebras $osp(1|2)$, $su(2|1)$ and $psu(2|2)$. Jacobi identities of supersymmetry algebras and associativities of star products are automatically satisfied. Covariant derivatives which commute with supersymmetry generators are obtained and chiral constraints can be imposed. We also discuss that these noncommutative superspaces can be understood as constrained systems analogous to the lowest Landau level system.

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