Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
arXiv:hep-th/9908040 · doi:10.1088/1126-6708/1999/09/023
Abstract
The geometry of D-branes can be probed by open string scattering. If the background carries a non-vanishing B-field, the world-volume becomes non-commutative. Here we explore the quantization of world-volume geometries in a curved background with non-zero Neveu-Schwarz 3-form field strength H = dB. Using exact and generally applicable methods from boundary conformal field theory, we study the example of open strings in the SU(2) Wess-Zumino-Witten model, and establish a relation with fuzzy spheres or certain (non-associative) deformations thereof. These findings could be of direct relevance for D-branes in the presence of Neveu-Schwarz 5-branes; more importantly, they provide insight into a completely new class of world-volume geometries.
19 pages, LaTeX, 1 figure; some explanations improved, references added
References in corpus (5)
Cited by in corpus (174)
- Noncommutative Field Theory
- M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
- Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
- D-Brane Instantons and K-Theory Charges
- Brane Dynamics in Background Fluxes and Non-commutative Geometry
- Nonassociative Star Product Deformations for D-brane Worldvolumes in Curved Backgrounds
- Symmetry, Gravity and Noncommutativity
- Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
- Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
- Nonassociative Gravity in String Theory?
- Scaling Limits of the Fuzzy Sphere at one Loop
- Coherent State Induced Star-Product on and the Fuzzy Sphere
- The geometry of WZW branes
- Permutation Branes
- Gauge Theory on a Quantum Phase Space
- Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
- Non-geometric backgrounds in string theory
- Nielsen-Olesen Vortices in Noncommutative Abelian Higgs Model
- Branes in the Euclidean AdS_3
- Noncommutative Harmonic Analysis, Sampling Theory and the Duflo Map in 2+1 Quantum Gravity
- Noncommutative geometry of angular momentum space U(su(2))
- Lectures on Non-BPS Dirichlet branes
- Field Theory on the q-deformed Fuzzy Sphere I
- M-theory branes and their interactions
- Infinitely many star products to play with
- D-Branes in the Background of NS Fivebranes
- Lectures on Branes in Curved Backgrounds
- Boundary States for the Rolling D-branes in NS5 Background
- Dirichlet Branes on Orbifolds
- F-theory and Dark Energy
- Noncommutative Superspace, Supermatrix and Lowest Landau Level
- Ramond-Ramond Flux Stabilization of D-Branes
- Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere
- Formation of Spherical D2-brane from Multiple D0-branes
- D-Branes in Coset Models
- Non-commutative geometry of 4-dimensional quantum Hall droplet
- On the hierarchy of symmetry breaking D-branes in group manifolds
- Noncommutative D-Brane in Non-Constant NS-NS B Field Background
- Monopole Bundles over Fuzzy Complex Projective Spaces
- Field Theory on the q-deformed Fuzzy Sphere II: Quantization
- Little Strings, Long Strings, and Fuzzballs
- Nonabelian Phenomena on D-branes
- Branes in the GL(1|1) WZNW-Model
- Some comments on Anti-de Sitter D-branes
- D-brane Solutions in Non-Commutative Gauge Theory on Fuzzy Sphere
- Open Strings on AdS_2 Branes
- Non-commutative gauge theory of twisted D-branes
- Fuzzy Complex Grassmannian Spaces and their Star Products
- Aspects of supertubes
- Noncommutative Model with Spontaneous Time Generation and Planckian bound
- Open Strings and Non-commutative Geometry of Branes on Group Manifolds
- Fundamental strings in Dp-Dq brane systems
- Multiloop String Amplitudes with B-Field and Noncommutative QFT
- Notes on Orientifolds of Rational Conformal Field Theories
- In search of conformal theories
- Evidence for F(uzz) Theory
- D-branes on group manifolds and fusion rings
- The deformation quantizations of the hyperbolic plane
- D-branes and BCFT in Hpp-wave backgrounds
- The Fuzzy Sphere Star-Product and Spin Networks
- Boundary States for D-branes in
- Noncommutative Differential Calculus for D-brane in Non-Constant B Field Background
- A Fuzzy Three Sphere and Fuzzy Tori
- Open Strings in Simple Current Orbifolds
- Quantum Fields with Noncommutative Target Spaces
- On Orientifolds of WZW Models and their Relation to Geometry
- Geometry of branes on supergroups
- Boundary Correlators in Supergroup WZNW Models
- Matrix Quantization of Gravitational Edge Modes
- Fuzzy Gravitons From Uncertain Spacetime
- A New Noncommutative Product on the Fuzzy Two-Sphere Corresponding to the Unitary Representation of SU(2) and the Seiberg-Witten Map
- Lectures on Matrix Field Theory I
- Matrix Models as Non-commutative Field Theories on R^3
- On the 1-loop effective action for the IKKT model and non-commutative branes
- Braided Symmetries in Noncommutative Field Theory
- Noncommutative Field Theory on Homogeneous Gravitational Waves
- Factorization Conjecture and the Open/Closed String Correspondence
- Non-Commutative Geometry from Strings
- Dirac Operator on the Quantum Sphere
- Quantum Field Theory in a Non-Commutative Space: Theoretical Predictions and Numerical Results on the Fuzzy Sphere
- Unbraiding the braided tensor product
- Tachyon Condensation on Fuzzy Sphere and Noncommutative Solitons
- A quantum algebraic description of D-branes on group manifolds
- Fuzzy Instantons
- Renormalization Group Analysis of Tachyon Condensation
- Quantum Black Holes: the Event Horizon as a Fuzzy Sphere
- Localization for Yang-Mills Theory on the Fuzzy Sphere
- Maximally symmetric D-branes in gauged WZW models
- Normal ordering and boundary conditions in open bosonic strings
- Towards Quantum Dielectric Branes: Curvature Corrections in Abelian Beta Function and Nonabelian Born-Infeld Action
- Myers Effect and Tachyon Condensation
- Brane Dynamics in CFT Backgrounds
- Nonassociativity and Integrable Hierarchies
- CP^n Model on Fuzzy Sphere
- Expanded Strings in the Background of NS5-branes via a M2-brane, a D2-brane and D0-branes
- D-branes on Group Manifolds and Deformation Quantization
- D1-Strings in Large RR 3-Form Flux, Quantum Nambu Geometry and M5-Branes in C-Field
- Noncommutative Gauge Theories from Deformation Quantization
- Hamiltonian Formulation of Open WZW Strings
- D-branes in Lie groups of rank > 1
- Supersymmetric Monopole Quantum Mechanics on Sphere
- Gravitational Dielectric Effect and Myers Effect
- Superconformal boundary conditions for the WZW model
- Boundary three-point function on AdS2 D-branes
- Noncommutativity in weakly curved background by canonical methods
- Orientifolds of SU(2)/U(1) WZW Models
- BRST construction of D-branes in SU(2) WZW model
- Aspects of M-Theory Brane Interactions and String Theory Symmetries
- Hidden classical symmetry in quantum spaces at roots of unity : From q-sphere to fuzzy sphere
- Scalar Multi-Solitons on the Fuzzy Sphere
- Normal ordering and non(anti)commutativity in open super strings
- Nongeometric background arising in the solution of Neumann boundary conditions
- Tachyon Lump Solutions of Bosonic D-branes on SU(2) Group Manifolds in Cubic String Field Theory
- Towards Gauge theory for a class of commutative and non-associative fuzzy spaces
- Thermodynamics on Fuzzy Spacetime
- Quantum Stabilization of Compact Space by Extra Fuzzy Space
- Bootstrapping Non-commutative Gauge Theories from L algebras
- Non-commutativity parameters depend not only on the effective coordinate but on its T-dual as well
- On the geometry of coset branes
- A complete solution of a Constrained System: SUSY Monopole Quantum Mechanics
- Defects, dualities and the geometry of strings via gerbes. I. Dualities and state fusion through defects
- Level-rank duality of untwisted and twisted D-branes
- Level-rank duality of D-branes on the SU(N) group manifold
- Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves
- D-branes in some near-horizon geometries
- D1 string dynamics in curved backgrounds with fluxes
- On DBI action of the non-maximally symmetric D-branes on SU(2)
- Closed constraint algebras and path integrals for loop group actions
- Blocking up D-branes : Matrix renormalization ?
- Marginal deformations and quasi-Hopf algebras
- Effective Action for D-branes on SU(2)/U(1) Gauged WZW Model
- Normal ordering and boundary conditions for fermionic string coordinates
- A fuzzy bipolar celestial sphere
- Coulomb-gas formulation of SU(2) branes and chiral blocks
- Nonstatic AdS_2 Branes and the Isometry Group of AdS_3 Spacetime
- A Note on Thermodynamics and Holography of Moving Giant Gravitons
- Effective Potential on Fuzzy Sphere
- Fuzzy hyperspheres via confining potentials and energy cutoffs
- Yang-Mills in non-commutative space time
- Non-commutativity in polar coordinates
- Invariant star-products on S^2 and the canonical trace
- Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions
- An Associative and Noncommutative Product for the Low Energy Effective Theory of a D-Brane in Curved Backgrounds and Bi-Local Fields
- YM on the dielectric brane: a D0-brane tale
- Quantum Matrix Models for Simple Current Orbifolds
- Strings, Dipoles and Fuzzy Spheres
- Field theoretic models on covariant quantum spaces
- Brane Bulk Couplings and Condensation from REA Fusion
- High-Energy Scattering in Non-Commutative Field Theory
- Non-commutative 4-spheres based on all Podleś 2-spheres and beyond
- Open string T-duality in a weakly curved background
- Twisted D-branes of the SU(N)_K WZW model and level-rank duality
- Deformations of anti-de Sitter black holes
- Non-commutative Weitzenboeck geometry, gerbe modules, and WZW branes
- On the Correspondence of Open and Closed Strings
- Inner brane: A D3-brane in the Nappi-Witten model from an inner group automorphism
- Quantum Energy of Fuzzy Sphere: Gaussian Variational Method
- Twisted WZW Branes from Twisted REA's
- Fuzzy sphere bimodule, ABS construction to the exact soliton solutions
- The universal envelope of the topological closed string BRST-complex
- D-branes with Lorentzian signature in the Nappi-Witten model
- D-Branes in Noncommutative Field Theory
- Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models
- Exotic smooth R^4, geometry of string backgrounds and quantum D-branes
- String Field Theory and the Fuzzy Sphere
- Open strings in Lie groups and associative products
- Bundles of chiral blocks and boundary conditions in CFT
- Level-rank duality of untwisted and twisted D-branes of the so(N)_K WZW model
- Generalized Dirichlet normal ordering in open bosonic strings
- Branes and Geometry in String and M-Theory
- D-branes, actions effectives et symétrie miroir
- Deformation Quantization and Quantum Field Theory on Curved Spaces: the Case of Two-Sphere
- Heat kernel expansion and induced action for matrix models
- Geometric construction of D-branes in WZW models