19 research outputs found
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
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
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
Z_2-Regge versus Standard Regge Calculus in two dimensions
We consider two versions of quantum Regge calculus. The Standard Regge
Calculus where the quadratic link lengths of the simplicial manifold vary
continuously and the Z_2-Regge Model where they are restricted to two possible
values. The goal is to determine whether the computationally more easily
accessible Z_2 model still retains the universal characteristics of standard
Regge theory in two dimensions. In order to compare observables such as average
curvature or Liouville field susceptibility, we use in both models the same
functional integration measure, which is chosen to render the Z_2-Regge Model
particularly simple. Expectation values are computed numerically and agree
qualitatively for positive bare couplings. The phase transition within the
Z_2-Regge Model is analyzed by mean-field theory.Comment: 21 pages, 16 ps-figures, to be published in Phys. Rev.
The Well-Defined Phase of Simplicial Quantum Gravity in Four Dimensions
We analyze simplicial quantum gravity in four dimensions using the Regge
approach. The existence of an entropy dominated phase with small negative
curvature is investigated in detail. It turns out that observables of the
system possess finite expectation values although the Einstein-Hilbert action
is unbounded. This well-defined phase is found to be stable for a one-parameter
family of measures. A preliminary study indicates that the influence of the
lattice size on the average curvature is small. We compare our results with
those obtained by dynamical triangulation and find qualitative correspondence.Comment: 29 pages, uuencoded postscript file; to appear in Phys. Rev.
Is There Quantum Gravity in Two Dimensions?
A hybrid model which allows to interpolate between the (original) Regge
approach and dynamical triangulations is introduced. The gained flexibility in
the measure is exploited to study dynamical triangulation in a fixed geometry.
Our numerical results support KPZ exponents. A critical assessment concerning
the apparent lack of gravitational effects in two dimensions follows.Comment: 20 pages including 4 figures, uuencoded Z-compressed .tar file
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