Field Theory on the q-deformed Fuzzy Sphere I

Abstract

We study the q-deformed fuzzy sphere, which is related to D-branes on SU(2) WZW models, for both real q and q a root of unity. We construct for both cases a differential calculus which is compatible with the star structure, study the integral, and find a canonical frame of one-forms. We then consider actions for scalar field theory, as well as for Yang-Mills and Chern-Simons-type gauge theories. The zero curvature condition is solved.

arXiv comment42 pages, 1 figure. Slight correction to reality condition for fields, typos corrected. To appear in Journ. Geom. Phys

References in corpus (23)

• String Theory and Noncommutative Geometry
• Noncommutative Perturbative Dynamics
• Noncommutative Open String and D-brane
• D-branes and the Noncommutative Torus
• Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
• Brane Dynamics in Background Fluxes and Non-commutative Geometry
• Perturbative quantum gauge fields on the noncommutative torus
• Field Theory on a Supersymmetric Lattice
• Field Theory on the q-deformed Fuzzy Sphere I
• Introduction to Braided Geometry and $q$-Minkowski Space
• Differential Calculi and Linear Connections
• Identical Particles and Quantum Symmetries
• Reality in the Differential Calculus on q-euclidean Spaces
• Quantum Group Gauge Theories and Covariant Quantum Algebras
• Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces
• The $S{O}_q(N,\mathbf{R})$-Symmetric Harmonic Oscillator on the Quantum Euclidean Space ${\mathbf{R}}_q^N$ and its Hilbert Space Structure
• Structure of the Three-dimensional Quantum Euclidean Space
• Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras
• Integration on quantum Euclidean space and sphere in $N$ dimensions
• Propagator on the h-deformed Lobachevsky plane
• More on quantum groups from the the quantization point of view
• Quantum Groups, Roots of Unity and Particles on quantized Anti-de Sitter Space
• Unitary Representations and BRST Structure of the Quantum Anti--de Sitter Group at Roots of Unity

Cited by in corpus (48)

• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Symmetry, Gravity and Noncommutativity
• Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
• Scaling Limits of the Fuzzy Sphere at one Loop
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Field Theory on the q-deformed Fuzzy Sphere I
• Cosmological Deformation of Lorentzian Spin Foam Models
• Monopole Bundles over Fuzzy Complex Projective Spaces
• Field Theory on the q-deformed Fuzzy Sphere II: Quantization
• Covariant Realization of Quantum Spaces as Star Products by Drinfeld Twists
• Matrix Models, Gauge Theory and Emergent Geometry
• The Fuzzy Sphere Star-Product and Spin Networks
• Drinfeld Twist and General Relativity with Fuzzy Spaces
• Braided Symmetries in Noncommutative Field Theory
• Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• Modified cosmology from quantum deformed entropy
• Unbraiding the braided tensor product
• A quantum algebraic description of D-branes on group manifolds
• On the Decoupling of the Homogeneous and Inhomogeneous Parts in Inhomogeneous Quantum Groups
• Ultra-violet Finite Noncommutative Theories
• Fuzzy Instantons
• Gromov-Hausdorff Distance for Quantum Metric Spaces
• Dirac operator on the q-deformed Fuzzy sphere and Its spectrum
• The Relativistic Avatars of Giant Magnons and their S-Matrix
• QFT with Twisted Poincaré Invariance and the Moyal Product
• Duality and Braiding in Twisted Quantum Field Theory
• Holographic Hierarchy in the Gaussian Matrix Model via the Fuzzy Sphere
• Algebraic brane dynamics on SU(2): excitation spectra
• Batalin-Vilkovisky quantization of fuzzy field theories
• Marginal deformations and quasi-Hopf algebras
• 'Schwinger Model' on the Fuzzy Sphere
• Index Theorem for the $q$-Deformed Fuzzy Sphere
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• Gauge Field Theory on the E_q(2)-covariant Plane
• On the physics of the $s{o}_q(4)$ hydrogen atom
• Quantum Mechanics on the Hypercube
• Jordanian quantum spheres
• A projective Dirac operator on CP^2 within fuzzy geometry
• q-Fuzzy spheres and quantum differentials on B_q[SU_2] and U_q(su_2)
• Fuzzy Torus and q-Deformed Lie Algebra
• Field theoretic models on covariant quantum spaces
• Quantum Matrix Models for Simple Current Orbifolds
• 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 $S_{qF}^4$
• Developments on the Jordan-Schwinger construction and contraction for the $s{u}_q(2)$
• The Garden of Quantum Spheres
• Noncommutative quantum analogs of constant curvature spaces