2003/06/30 by Machiko Hatsuda, Satoshi Iso, Hiroshi Umetsu · 2 citations
Mathematics · Physics and Astronomy · #Affine Lie algebra #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Covariant transformation #F-term #Lie algebra #Mathematical physics #Mathematics #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Pure mathematics #Supermatrix #Superspace #Supersymmetry #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2003.08.013
published as Nucl.Phys. B671 (2003) 217-242 · 29 pages, Latex. A subsection is added to explain the Seiberg's noncommutative superspace as a constrained system
arxiv created 2003/07/03 · openalex publication_date 2003/09/17 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.