# Dirac operator on fuzzy AdS2

@article{Fakhri2003DiracOO, title={Dirac operator on fuzzy AdS2}, author={Hossein Fakhri and Ali Imaanpur}, journal={Journal of High Energy Physics}, year={2003}, volume={2003}, pages={003} }

In this article we construct the chirality and Dirac operators on fuzzy AdS2. We also derive the discrete spectrum of the Dirac operator which is important in the study of the spectral triple associated to AdS2. It is shown that the degeneracy of the spectrum present in the commutative AdS2 is lifted in the noncommutative case. The way we construct the chirality operator is suggestive of how to introduce the projector operators of the corresponding projective modules on this space.

#### 12 Citations

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$$q$$
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$$EAdS^2$$
using a generalized
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-deformed Ginsparg–Wilson algebra

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Abstract We construct $$q$$ -deformed Dirac and chirality operators on the $$q$$ -deformed quantum space $$EAdS^2$$ using a generalized quantum Ginsparg–Wilson algebra. We show that in the limit… Expand

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#### References

SHOWING 1-10 OF 19 REFERENCES

Chirality and Dirac operator on noncommutative sphere

- Physics, Mathematics
- 1996

We give a derivation of the Dirac operator on the noncommutative 2-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types… Expand

THE DIRAC OPERATOR ON HYPERSURFACES

- Mathematics, Physics
- 1995

Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here… Expand

Noncommutative Geometry¶and Gauge Theory on Fuzzy Sphere

- Mathematics, Physics
- 2000

Abstract: The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined. The local… Expand

Quantum Mechanics on Noncommutative Riemann Surfaces

- Physics, Mathematics
- 2002

Abstract We study the quantum mechanics of a charged particle on a constant curvature noncommutative Riemann surface in the presence of a constant magnetic field. We formulate the problem by… Expand

Large N expansion from fuzzy AdS(2)

- Physics
- 2000

We study the quantum analogue of primary fields and their descendants on fuzzy AdS(2). Three-point vertices are calculated and shown to exhibit the conventional 1/N expansion as well as… Expand

Eigenvalue estimates for the Dirac–Schrödinger operators

- Mathematics
- 2001

Abstract We give new estimates for the eigenvalues of the hypersurface Dirac operator in terms of the intrinsic energy–momentum tensor, the mean curvature and the scalar curvature. We also discuss… Expand

Solution of the Dirac equation on the homogeneous manifold SL(2,c)/GL(1,c) in the presence of a magnetic monopole field

- Physics
- 2000

Equations of shape invariance have been derived on the homogeneous manifold SL (2,c )/GL (1,c ), by means of which the Dirac equation is solved for a charged spin-½ particle in the presence of a… Expand

Dirac equation for a spin-? charged particle on the 2D sphere S2 and the hyperbolic plane H2

- Physics
- 2002

Using the idea of shape invariance with respect to the main quantum number n, we represent Lie algebras u(2) and u(1, 1). The induced metric by the Casimir operator of Lie algebras u(2) and u(1, 1)… Expand

Deconstructing Monopoles and Instantons

- Mathematics, Physics
- 1998

We give a unifying description of the Dirac monopole on the 2-sphere S2, of a graded monopole on a (2, 2)-supersphere S2, 2 and of the BPST instanton on the 4-sphere S4, by constructing a suitable… Expand

Monopoles and Solitons in Fuzzy Physics

- Physics, Mathematics
- 2000

Abstract:Monopoles and solitons have important topological aspects like quantized fluxes, winding numbers and curved target spaces. Naive discretizations which substitute a lattice of points for the… Expand