165 research outputs found
Modified gravity without new degrees of freedom
We show that the new type of "non-metric" gravity theories introduced
independently by Bengtsson and Krasnov can in fact be reexpressed explicitely
as a metrical theory coupled to an auxiliary field. We unravel why such
theories possess only one propagating graviton by looking at the quadratic
perturbation around a fixed solution. And we give a general construction
principle with a new class of example of such modified gravity theories still
possessing only two propagating degrees of freedom.Comment: 19 page
From sl(2) Kirby weight systems to the asymptotic 3-manifold invariant
We give a construction of Kirby weight systems associated to sl(2) and valued
into the finite field Z/pZ. We show that it is possible to apply this sequence
of weight systems on the universal invariant of framed link. We also show that
the corresponding sequence admits a Fermat limit, which defines an asymptotic
rational homology 3-sphere quantum invariant. Moreover, this asymptotic
invariant coincides with the Ohtsuki invariant.Comment: 27 pages, 19 figures, added reference
Gravitational Energy, Local Holography and Non-equilibrium Thermodynamics
We study the properties of gravitational system in finite regions bounded by
gravitational screens. We present the detail construction of the total energy
of such regions and of the energy and momentum balance equations due to the
flow of matter and gravitational radiation through the screen. We establish
that the gravitational screen possesses analogs of surface tension, internal
energy and viscous stress tensor, while the conservations are analogs of
non-equilibrium balance equations for a viscous system. This gives a precise
correspondence between gravity in finite regions and non-equilibrium
thermodynamics.Comment: 41 pages, 3 figure
Lorentz invariant deformations of momentum space
In relative locality theories the geometric properties of phase space depart
from the standard ones given by the fact that spaces of momenta are linear
fibers over a spacetime base manifold. In particular here it is assumed that
the momentum space is non linear and can therefore carry non trivial metric and
composition law. We classify to second order all possible such deformations
that preserve Lorentz invariance. We show that such deformations still exists
after quotienting out by diffeomorphisms only if the non linear addition is non
associative.Comment: 6 page
On Universal Vassiliev Invariants
Using properties of ordered exponentials and the definition of the Drinfeld
associator as a monodromy operator for the Knizhnik-Zamolodchikov equations, we
prove that the analytic and the combinatorial definitions of the universal
Vassiliev invariants of links are equivalent.Comment: 33 page
Quantum gravity at the corner
We investigate the quantum geometry of surface bounding the Cauchy
slices of 4d gravitational system. We investigate in detail and for the first
time the symplectic current that naturally arises boundary term in the first
order formulation of general relativity in terms of the Ashtekar-Barbero
connection. This current is proportional to the simplest quadratic form
constructed out of the triad field, pulled back on . We show that the
would-be-gauge degrees of freedom---arising from gauge transformations
plus diffeomorphisms tangent to the boundary, are entirely described by the
boundary -dimensional symplectic form and give rise to a representation at
each point of of . Independently of the
connection with gravity, this system is very simple and rich at the quantum
level with possible connections with conformal field theory in 2d. A direct
application of the quantum theory is modelling of the black horizons in quantum
gravity
Local subsystems in gauge theory and gravity
We consider the problem of defining localized subsystems in gauge theory and
gravity. Such systems are associated to spacelike hypersurfaces with boundaries
and provide the natural setting for studying entanglement entropy of regions of
space. We present a general formalism to associate a gauge-invariant classical
phase space to a spatial slice with boundary by introducing new degrees of
freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a
choice of gauge on the boundary, transformations of which are generated by the
normal component of the nonabelian electric field. In general relativity the
new degrees of freedom are the location of a codimension-2 surface and a choice
of conformal normal frame. These degrees of freedom transform under a group of
surface symmetries, consisting of diffeomorphisms of the codimension-2
boundary, and position-dependent linear deformations of its normal plane. We
find the observables which generate these symmetries, consisting of the
conformal normal metric and curvature of the normal connection. We discuss the
implications for the problem of defining entanglement entropy in quantum
gravity. Our work suggests that the Bekenstein-Hawking entropy may arise from
the different ways of gluing together two partial Cauchy surfaces at a
cross-section of the horizon.Comment: 46 pages. v2: Error corrected in appendix B, results unchange
Spin Foam Models and the Classical Action Principle
We propose a new systematic approach that allows one to derive the spin foam
(state sum) model of a theory starting from the corresponding classical action
functional. It can be applied to any theory whose action can be written as that
of the BF theory plus a functional of the B field. Examples of such theories
include BF theories with or without cosmological term, Yang-Mills theories and
gravity in various spacetime dimensions. Our main idea is two-fold. First, we
propose to take into account in the path integral certain distributional
configurations of the B field in which it is concentrated along lower
dimensional hypersurfaces in spacetime. Second, using the notion of generating
functional we develop perturbation expansion techniques, with the role of the
free theory played by the BF theory. We test our approach on various theories
for which the corresponding spin foam (state sum) models are known. We find
that it exactly reproduces the known models for BF and 2D Yang-Mills theories.
For the BF theory with cosmological term in 3 and 4 dimensions we calculate the
terms of the transition amplitude that are of the first order in the
cosmological constant, and find an agreement with the corresponding first order
terms of the known state sum models. We discuss implications of our results for
existing quantum gravity models.Comment: 65 pages, many figures (published version
Non-perturbative summation over 3D discrete topologies
We construct a group field theory which realizes the sum of gravity
amplitudes over all three dimensional topologies trough a perturbative
expansion. We prove this theory to be uniquely Borel summable. This shows how
to define a non-perturbative summation over triangulations including all
topologies in the context of three dimensional discrete gravity.Comment: 20 pages, 9 figures, note added, minor correction
A Discrete and Coherent Basis of Intertwiners
We construct a new discrete basis of 4-valent SU(2) intertwiners. This basis
possesses both the advantage of being discrete, while at the same time
representing accurately the classical degrees of freedom; hence it is coherent.
The closed spin network amplitude obtained from these intertwiners depends on
twenty spins and can be evaluated by a generalization of the Racah formula for
an arbitrary graph. The asymptotic limit of these amplitudes is found. We give,
for the first time, the asymptotics of 15j symbols in the real basis.
Remarkably it gives a generalization of the Regge action to twisted geometries
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