Dirac Operator on Fuzzy AdS_2

Abstract

In this article we construct the chirality and Dirac operators on noncommutative AdS_2. We also derive the discrete spectrum of the Dirac operator which is important in the study of the spectral triple associated with AdS_2. It is shown that the degeneracy of the spectrum present in the commutative AdS_2 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.

latex, 16 pages, no figure, added a reference and minor changes

References in corpus (11)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Monopoles and Solitons in Fuzzy Physics
• Noncommutative Geometry and Gauge Theory on Fuzzy Sphere
• Chirality and Dirac Operator on Noncommutative Sphere
• Quantum mechanics on noncommutative Riemann surfaces
• Eigenvalue estimates for the Dirac-Schrödinger operators
• Large N Expansion From Fuzzy AdS_2

Cited by in corpus (6)

• Quantized Nambu-Poisson Manifolds and n-Lie Algebras
• Non-Compact Hopf Maps and Fuzzy Ultra-Hyperboloids
• Non-constant Non-commutativity in 2d Field Theories and a New Look at Fuzzy Monopoles
• Exact solutions for scalars and spinors on quantized (Euclidean) $Ad{S}_2$ and the correspondence principle
• Super quantum Dirac operator on the q-deformed super fuzzy sphere in instanton sector using quantum super Ginsparg-Wilson algebra
• Dirac operator on the quantum fuzzy four-sphere $S_{qF}^4$