Matrix D-brane Dynamics, Logarithmic Operators and Quantization of Noncommutative Spacetime

Abstract

We describe the structure of the moduli space of $\sigma$-model couplings for the worldsheet description of a system of $N$ D-particles, in the case that the couplings are represented by a pair of logarithmic recoil operators. We derive expressions for the canonical momenta conjugate to the D-particle couplings and the Zamolodchikov metric to the first few orders in $\sigma$-model perturbation theory. We show, using only very general properties of the operator product expansion in logarithmic conformal field theories, that the canonical dynamics on moduli space agree with the predictions of the non-abelian generalization of the Born-Infeld effective action for D-particles with a symmetrized trace structure. We demonstrate that the Zamolodchikov metric naturally encodes the short-distance structure of spacetime, and from this we derive uncertainty relations for the D-particle coordinates directly from the quantum string theory. We show that the moduli space geometry naturally leads to new forms of spacetime indeterminancies involving only spatial coordinates of target space and illustrate the manner in which the open string interactions between D-particles lead to a spacetime quantization. We also derive appropriate non-abelian generalizations of the string-modified Heisenberg uncertainty relations and the space--time uncertainty principle. The non-abelian uncertainties exhibit decoherence effects suggesting the interplay of quantum gravity in multiple D-particle dynamics.

67 pages LATEX, three eps figures incorporated

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Cited by in corpus (68)

• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review
• Astrophysical Probes of the Constancy of the Velocity of Light
• Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model
• World-Volume Interactions on D-Branes
• Synchrotron Radiation from the Crab Nebula Discriminates between Models of Space-Time Foam
• A Microscopic Recoil Model for Light-Cone Fluctuations in Quantum Gravity
• A supersymmetric D-brane Model of Space-Time Foam
• Dynamical Formation of Horizons in Recoiling D Branes
• Gravitational-Recoil Effects on Fermion Propagation in Space-Time Foam
• Implications of a Stochastic Microscopic Finsler Cosmology
• Holographic applications of logarithmic conformal field theories
• Space-Time Foam Effects on Particle Interactions and the GZK Cutoff
• Liouville Cosmology at Zero and Finite Temperatures
• Space-Time Foam may Violate the Principle of Equivalence
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Stringy Space-Time Foam, Finsler-like Metrics and Dark Matter Relics
• Magnetic Backgrounds and Noncommutative Field Theory
• String Quantum Gravity, Lorentz-Invariance Violation and Gamma-Ray Astronomy
• Operator Product Expansion in Logarithmic Conformal Field Theory
• How Large are Dissipative Effects in Non-Critical Liouville String Theory?
• Logarithmic Conformal Field Theory and Seiberg-Witten Models
• Quantum-Gravity Induced Lorentz Violation and Dynamical Mass Generation
• Relativistic Modified Newtonian Dynamics from String Theory?
• Vacuum Energy and Cosmological Supersymmetry Breaking in Brane Worlds
• Flavour Condensates in Brane Models and Dark Energy
• Lorentz Invariance Violation from String Theory
• CPT Violation and Decoherence in Quantum Gravity
• Brany Liouville Inflation
• Boundary states in boundary logarithmic CFT
• Decoherence and CPT Violation in a Stringy Model of Space-Time Foam
• The Neveu-Schwarz and Ramond Algebras of Logarithmic Superconformal Field Theory
• Worldvolume Uncertainty Relations for D-Branes
• Disordered Systems and Logarithmic Conformal Field Theory
• Non-Critical Liouville String Escapes Constraints on Generic Models of Quantum Gravity
• Light Speed Variation with Brane/String-Inspired Space-Time Foam
• Legendre's Relation and the Quantum Equivalence osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0)
• Non-extensive statistics in stringy space-time foam models and entangled meson states
• Logarithmic Currents in the SU(2)_0 WZNW model
• Logarithmic Operators Fold D branes into AdS_3
• Stringy Models of Modified Gravity: Space-time defects and Structure Formation
• D-Brane Recoil and Supersymmetry Obstruction
• Non-linear Schroedinger Dynamics of Matrix D-branes
• Logarithmic Conformal Field Theories and Strings in Changing Backgrounds
• Light-Cone Broadening and TeV Scale Extra Dimensions
• A mass hierarchy from recoiling D branes
• Lorentz and CPT breaking in gamma-ray burst neutrinos from string theory
• The O(n) Model in the $n\to 0$ Limit (self-avoiding-walks) and Logarithmic Conformal Field Theory
• Neutrino oscillations in a Robertson-Walker Universe with space time foam
• D-branes and Azumaya/matrix noncommutative differential geometry,II: Azumaya/matrix supermanifolds and differentiable maps therefrom -- with a view toward dynamical fermionic D-branes in string theory
• BUSSTEPP Lectures on String Theory
• D-Brane Recoil and Supersymmetry Breaking as a Relaxation Process
• Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
• Recoiling D-branes
• A Novel Mass Hierarchy and Discrete Excitation Spectra from Quantum-Fluctuating D-branes
• Probes for String-Inspired Foam, Lorentz, and CPT Violations in Astrophysics
• Effects on neutrino propagation in space-time foam of D-branes revisited
• Stringy Space-Time Foam and High-Energy Cosmic Photons
• Local Currents for a Deformed Algebra of Quantum Mechanics with a Fundamental Length Scale
• A Novel Foamy Origin for Singlet Fermion Masses
• Two-Point Functions and Logarithmic Boundary Operators in Boundary Logarithmic Conformal Field Theories
• Two-Point Functions and Boundary States in Boundary Logarithmic Conformal Field Theories
• Constraints to Lorentz violation and ultrahigh-energy electrons in D-foamy space-times
• The Omega Effect for Neutral Mesons
• N=1/2 Global SUSY: R-Matrix Approach
• Constraining D-foam via the 21-cm Line
• The String Coupling Accelerates the Expansion of the Universe
• Flavour Condensate and the Dark Sector of the Universe