Extended 2d generalized dilaton gravity theories

Abstract

We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2d relativity principle, which introduces a non-trivial center in the 2d Poincare algebra. Then we work out the reduced phase-space of the anomaly-free 2d relativistic particle, in order to show that it lives in a noncommutative 2d Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well-defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2d generalized dilaton gravity models by a specific Maxwell component, which gauges the extra symmetry associated with the center of the 2d Poincare algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of space-time. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved space-time, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides a strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson-Sigma models based on a nonlinear deformation of the extended Poincare algebra.

21 pages, IOP LaTeX2e preprint classfile, Improved discussions, Minor corrections, More didactic, More self-contained, New results concerning noncommutativity in curved space-time, Accepted for publication in Classical and Quantum Gravity on 02 Jul 2008

References in corpus (21)

• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Space-Time Noncommutative Field Theories And Unitarity
• Dilaton Gravity in Two Dimensions
• Poisson Structure Induced (Topological) Field Theories
• Non-linear finite $W$-symmetries and applications in elementary systems
• Exact Path Integral Quantization of Generic 2-D Dilaton Gravity
• The Classical Solutions of the Dimensionally Reduced Gravitational Chern-Simons Theory
• General Form of Dilaton Gravity and Nonlinear Gauge Theory
• Poincaré Gauge Theory for Gravitational Forces in (1+1) Dimensions
• Integrating Geometry in General 2D Dilaton Gravity with Matter
• Gauge Theories for Gravity on a Line
• An action for the exact string black hole
• Observations on noncommuting coordinates and on fields depending on them
• Black Hole Thermodynamics and Two-Dimensional Dilaton Gravity Theory
• Quantum Dilaton Gravity in Two Dimensions with Fermionic Matter
• Extended de Sitter Theory of Two Dimensional Gravitational Forces
• Stability of a Noncommutative Jackiw-Teitelboim Gravity
• Logarithmic corrections to the entropy of the exact string black hole
• The irreducible unitary representations of the extended Poincare group in (1+1) dimensions
• Entropy of the 3-brane and the AdS/CFT duality from a two-dimensional perspective