55,988 research outputs found
Uniformizing higher-spin equations
Vasiliev's higher-spin theories in various dimensions are uniformly
represented as a simple system of equations. These equations and their gauge
invariances are based on two superalgebras and have a transparent algebraic
meaning. For a given higher-spin theory these algebras can be inferred from the
vacuum higher-spin symmetries. The proposed system of equations admits a
concise AKSZ formulation. We also discuss novel higher-spin systems including
partially-massless and massive fields in AdS, as well as conformal and massless
off-shell fields.Comment: 29 pages, references added, final versio
Higher-Spin Theory and Space-Time Metamorphoses
Introductory lectures on higher-spin gauge theory given at 7 Aegean workshop
on non-Einstein theories of gravity. The emphasis is on qualitative features of
the higher-spin gauge theory and peculiarities of its space-time
interpretation. In particular, it is explained that Riemannian geometry cannot
play a fundamental role in the higher-spin gauge theory. The higher-spin
symmetries are argued to occur at ultra high energy scales beyond the Planck
scale. This suggests that the higher-spin gauge theory can help to understand
Quantum Gravity. Various types of higher-spin dualities are briefly discussed.Comment: 37 pages, no figures; V2: references adde
Extended 2d generalized dilaton gravity theories
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.Comment: 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 200
Quantized Nambu-Poisson Manifolds and n-Lie Algebras
We investigate the geometric interpretation of quantized Nambu-Poisson
structures in terms of noncommutative geometries. We describe an extension of
the usual axioms of quantization in which classical Nambu-Poisson structures
are translated to n-Lie algebras at quantum level. We demonstrate that this
generalized procedure matches an extension of Berezin-Toeplitz quantization
yielding quantized spheres, hyperboloids, and superspheres. The extended
Berezin quantization of spheres is closely related to a deformation
quantization of n-Lie algebras, as well as the approach based on harmonic
analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms
of foliations of R^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative
hyperplanes. Some applications to the quantum geometry of branes in M-theory
are also briefly discussed.Comment: 43 pages, minor corrections, presentation improved, references adde
Symmetry, Gravity and Noncommutativity
We review some aspects of the implementation of spacetime symmetries in
noncommutative field theories, emphasizing their origin in string theory and
how they may be used to construct theories of gravitation. The geometry of
canonical noncommutative gauge transformations is analysed in detail and it is
shown how noncommutative Yang-Mills theory can be related to a gravity theory.
The construction of twisted spacetime symmetries and their role in constructing
a noncommutative extension of general relativity is described. We also analyse
certain generic features of noncommutative gauge theories on D-branes in curved
spaces, treating several explicit examples of superstring backgrounds.Comment: 52 pages; Invited review article to be published in Classical and
Quantum Gravity; v2: references adde
Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations
We present a possibility of coupling a point-like, non-singular, mass
distribution to four-dimensional quantum gravity in the nonperturbative setting
of causal dynamical triangulations (CDT). In order to provide a point of
comparison for the classical limit of the matter-coupled CDT model, we derive
the spatial volume profile of the Euclidean Schwarzschild-de Sitter space glued
to an interior matter solution. The volume profile is calculated with respect
to a specific proper-time foliation matching the global time slicing present in
CDT. It deviates in a characteristic manner from that of the pure-gravity
model. The appearance of coordinate caustics and the compactness of the mass
distribution in lattice units put an upper bound on the total mass for which
these calculations are expected to be valid. We also discuss some of the
implementation details for numerically measuring the expectation value of the
volume profiles in the framework of CDT when coupled appropriately to the
matter source.Comment: 26 pages, 9 figures, updated published versio
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