64 research outputs found
Regge gravity on general triangulations
We investigate quantum gravity in four dimensions using the Regge approach on
triangulations of the four-torus with general, non-regular incidence matrices.
We find that the simplicial lattice tends to develop spikes for vertices with
low coordination numbers even for vanishing gravitational coupling. Different
to the regular, hypercubic lattices almost exclusively used in previous
studies, we find now that the observables depend on the measure. Computations
with nonvanishing gravitational coupling still reveal the existence of a region
with well-defined expectation values. However, the phase structure depends on
the triangulation. Even with additional higher- order terms in the action the
critical behavior of the system changes with varying (local) coordination
numbers.Comment: uuencoded postscript file, 16 page
Two-Point Functions of Four-Dimensional Simplicial Quantum Gravity
We investigate the interaction mechanism of pure quantum gravity in Regge
discretization. We compute volume-volume and link-link correlation functions.
In a preliminary analysis the forces turn out to be of Yukawa type, at least on
our finite lattice being away from the continuum limit.Comment: 3 pages, uuencoded postscript file; Proceedings of the XI
International Symposion on Lattice Field Theory, Dallas, Oct. 199
SU(2) potentials in quantum gravity
We present investigations of the potential between static charges from a
simulation of quantum gravity coupled to an SU(2) gauge field on and simplicial lattices. In the well-defined phase of the
gravity sector where geometrical expectation values are stable, we study the
correlations of Polyakov loops and extract the corresponding potentials between
a source and sink separated by a distance . In the confined phase, the
potential has a linear form while in the deconfined phase, a screened Coulombic
behavior is found. Our results indicate that quantum gravitational effects do
not destroy confinement due to non-abelian gauge fields.Comment: 3 pages, contribution to Lattice 94 conference, uuencoded compressed
postscript fil
Static Quark Potentials in Quantum Gravity
We present potentials between static charges from simulations of quantum
gravity coupled to an SU(2) gauge field on and
simplicial lattices. The action consists of the gravitational term given by
Regge's discrete version of the Euclidean Einstein action and a gauge term
given by the Wilson action, with coupling constants and
respectively. In the well-defined phase of the gravity sector where geometrical
expectation values are stable, we study the correlations of Polyakov loops and
extract the corresponding potentials between a source and sink separated by a
distance . We compare potentials on a flat simplicial lattice with those on
a fluctuating Regge skeleton. In the confined phase, the potential has a linear
form while in the deconfined phase, a screened Coulombic behavior is found. Our
results indicate that quantum gravitational effects do not destroy confinement
due to non-abelian gauge fields.Comment: 8 pages, to be published in Phys. Lett. B, uuencoded compressed
postscript file
On the Continuum Limit of the Discrete Regge Model in 4d
The Regge Calculus approximates a continuous manifold by a simplicial
lattice, keeping the connectivities of the underlying lattice fixed and taking
the edge lengths as degrees of freedom. The Discrete Regge model employed in
this work limits the choice of the link lengths to a finite number. This makes
the computational evaluation of the path integral much faster. A main concern
in lattice field theories is the existence of a continuum limit which requires
the existence of a continuous phase transition. The recently conjectured
second-order transition of the four-dimensional Regge skeleton at negative
gravity coupling could be such a candidate. We examine this regime with Monte
Carlo simulations and critically discuss its behavior.Comment: Lattice2002(gravity
Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory
We analyze Regge quantum gravity coupled to SU(2) gauge theory on , and simplicial lattices. It turns out that
the window of the well-defined phase of the gravity sector where geometrical
expectation values are stable extends to negative gravitational couplings as
well as to gauge couplings across the deconfinement phase transition. We study
the string tension from Polyakov loops, compare with the -function of
pure gauge theory and conclude that a physical limit through scaling is
possible.Comment: RevTeX, 14 pages, 5 figures (2 eps, 3 tex), 2 table
Two-Dimensional Lattice Gravity as a Spin System
Quantum gravity is studied in the path integral formulation applying the
Regge calculus. Restricting the quadratic link lengths of the originally
triangular lattice the path integral can be transformed to the partition
function of a spin system with higher couplings on a Kagome lattice. Various
measures acting as external field are considered. Extensions to matter fields
and higher dimensions are discussed.Comment: 3 pages, uuencoded postscript file; Proceedings of the 2nd IMACS
Conference on Computational Physics, St. Louis, Oct. 199
Indications for Criticality at Zero Curvature in a 4d Regge Model of Euclidean Quantum Gravity
We re-examine the approach to four-dimensional Euclidean quantum gravity
based on the Regge calculus. A cut-off on the link lengths is introduced and
consequently the gravitational coupling and the cosmological constant become
independent parameters. We determine the zero curvature, , line in the
coupling constant plane by numerical simulations. When crossing this line we
find a strong, probably first order, phase transition line with indications of
a second order endpoint. Beyond the endpoint the transition through the line appears to be a crossover. Previous investigations, using the Regge or
the Dynamical Triangulation approach, dealt with a limit in which the first
order transition prevails.Comment: Contribution to the lattice 2003 Tsukuba symposiu
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