The fuzzy supersphere

Grosse, Harald; Reiter, G.

doi:10.1016/s0393-0440(98)00023-0

Cited by 38 publications

(48 citation statements)

References 45 publications

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“…Also in [GKP96], there is a study of fermions and supersymmetric extensions of the fuzzy sphere. An extensive treatment of the approximation of super-graded functions over the super sphere, and sections of a bundle through sequences of graded modules, as well as the treatment of the graded de Rham complex, is given in [GR98]. The description of the monopole on the super sphere that we provide can be related to that given in [BBL90].…”

Section: )mentioning

confidence: 99%

Strong Connections and Chern-Connes Pairing¶in the Hopf-Galois Theory

Da̧browski¹,

Grosse²,

Hajac

2001

Communications in Mathematical Physics

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We reformulate the concept of connection on a Hopf-Galois extension B ⊆ P in order to apply it in computing the Chern-Connes pairing between the cyclic cohomology HC 2n (B) and K 0 (B). This reformulation allows us to show that a Hopf-Galois extension admitting a strong connection is projective and left faithfully flat. It also enables us to conclude that a strong connection is a Cuntz-Quillen-type bimodule connection. To exemplify the theory, we construct a strong connection (super Dirac monopole) to find out the Chern-Connes pairing for the super line bundles associated to super Hopf fibration.

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Section: )mentioning

confidence: 99%

Strong Connections and Chern-Connes Pairing¶in the Hopf-Galois Theory

Da̧browski¹,

Grosse²,

Hajac

2001

Communications in Mathematical Physics

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“…The latter have been studied in the articles by Grosse et al [12,14]. Our formulation of the problem will be based on [12] for the properties of the fuzzy S (2,2) F and the work [9] for the introduction of the ⋆-product.…”

Section: Introductionmentioning

confidence: 99%

The Star Product on the Fuzzy Supersphere

Balachandran

Kürkçüoğlu

Rojas

2002

J. High Energy Phys.

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The fuzzy supersphere S (2,2) F is a finite-dimensional matrix approximation to the supersphere S (2,2) 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 (2,2) 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.

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“…The latter relation reflects the non-anti-commutative geometry in the SUSY LLL. The fuzzy super manifold introduced by the algebraic relation (4.2) is known as the fuzzy supersphere [36,37] 7 . Thus, SUSY NCG are nicely realized in the formulation of the SUSY QHE.…”

Section: The Spherical Susy Laughlin Wavefunction and Excitations [35]mentioning

confidence: 99%

SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry

Hasebe¹

2008

SIGMA

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Abstract. We review the recent developments of the SUSY quantum Hall effect [hep-th/0409230, hep-th/0411137, hep-th/0503162, hep-th/0606007, arXiv:0705.4527]. We introduce a SUSY formulation of the quantum Hall effect on supermanifolds. On each of supersphere and superplane, we investigate SUSY Landau problem and explicitly construct SUSY extensions of Laughlin wavefunction and topological excitations. The non-anticommutative geometry naturally emerges in the lowest Landau level and brings particular physics to the SUSY quantum Hall effect. It is shown that SUSY provides a unified picture of the original Laughlin and Moore-Read states. Based on the charge-flux duality, we also develop a Chern-Simons effective field theory for the SUSY quantum Hall effect.

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The fuzzy supersphere

Cited by 38 publications

References 45 publications

Strong Connections and Chern-Connes Pairing¶in the Hopf-Galois Theory

Strong Connections and Chern-Connes Pairing¶in the Hopf-Galois Theory

The Star Product on the Fuzzy Supersphere

SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry

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