The Star Product on the Fuzzy Supersphere
نویسنده
چکیده
The fuzzy supersphere S (2,2) F is a finite-dimensional matrix approximation to the supersphere S incorporating supersymmetry exactly. Here the ⋆-product of functions on S (2,2) F is obtained by utilizing the OSp(2, 1) coherent states. We check its graded commutative limit to S and extend it to fuzzy versions of sections of bundles using the methods of [1]. A brief discussion of the geometric structure of our ⋆-product completes our work. E-mails: [email protected], [email protected], [email protected]
منابع مشابه
Institute for Mathematical Physics the Fuzzy Supersphere the Fuzzy Supersphere
We introduce the fuzzy supersphere as sequence of nite-dimensional, noncommu-tative Z 2-graded algebras tending in a suitable limit to a dense subalgebra of the Z 2-graded algebra of H 1-functions on the (2j2)-dimensional supersphere. Noncom-mutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the supe...
متن کاملThe Fuzzy Supersphere
We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative Z2-graded algebras tending in a suitable limit to a dense subalgebra of the Z2-graded algebra of H∞-functions on the (2|2)-dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the superde...
متن کاملNote on Gauge Theory on Fuzzy Supersphere
We construct a supermatrix model whose classical background gives two-dimensional noncommutative supersphere. Quantum fluctuations around it give the supersymmetric gauge theories on the fuzzy supersphere constructed by Klimcik. This model has a parameter β which can tune masses of the particles in the model and interpolate various supersymmetric gauge theories on sphere.
متن کاملar X iv : m at h - ph / 9 80 40 13 v 1 2 1 A pr 1 99 8 The Fuzzy Supersphere
We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommu-tative Z 2-graded algebras tending in a suitable limit to a dense subalgebra of the Z 2-graded algebra of H ∞-functions on the (2|2)-dimensional supersphere. Noncom-mutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the su...
متن کاملGauge Theory on Noncommutative Supersphere from Supermatrix Model
We construct a supermatrix model which has a classical solution representing the noncommutative (fuzzy) two-supersphere. Expanding supermatrices around the classical background, we obtain a gauge theory on a noncommutative superspace on sphere. This theory has osp(1|2) supersymmetry and u(2L+1|2L) gauge symmetry. We also discuss a commutative limit of the model keeping radius of the supersphere...
متن کامل