5 research outputs found
Gravitational Wilson Loop and Large Scale Curvature
In a quantum theory of gravity the gravitational Wilson loop, defined as a
suitable quantum average of a parallel transport operator around a large
near-planar loop, provides important information about the large-scale
curvature properties of the geometry. Here we shows that such properties can be
systematically computed in the strong coupling limit of lattice regularized
quantum gravity, by performing a local average over rotations, using an assumed
near-uniform measure in group space. We then relate the resulting quantum
averages to an expected semi-classical form valid for macroscopic observers,
which leads to an identification of the gravitational correlation length
appearing in the Wilson loop with an observed large-scale curvature. Our
results suggest that strongly coupled gravity leads to a positively curved (De
Sitter-like) quantum ground state, implying a positive effective cosmological
constant at large distances.Comment: 22 pages, 6 figure
Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice
We present exact solutions for the zero-temperature partition function of the
-state Potts antiferromagnet (equivalently, the chromatic polynomial ) on
tube sections of the simple cubic lattice of fixed transverse size and arbitrarily great length , for sizes and and boundary conditions (a) and (b)
, where () denote free (periodic) boundary
conditions. In the limit of infinite-length, , we calculate the
resultant ground state degeneracy per site (= exponent of the ground-state
entropy). Generalizing from to , we determine
the analytic structure of and the related singular locus which
is the continuous accumulation set of zeros of the chromatic polynomial. For
the limit of a given family of lattice sections, is
analytic for real down to a value . We determine the values of
for the lattice sections considered and address the question of the value of
for a -dimensional Cartesian lattice. Analogous results are presented
for a tube of arbitrarily great length whose transverse cross section is formed
from the complete bipartite graph .Comment: 28 pages, latex, six postscript figures, two Mathematica file
Non-Perturbative Gravity and the Spin of the Lattice Graviton
The lattice formulation of quantum gravity provides a natural framework in
which non-perturbative properties of the ground state can be studied in detail.
In this paper we investigate how the lattice results relate to the continuum
semiclassical expansion about smooth manifolds. As an example we give an
explicit form for the lattice ground state wave functional for semiclassical
geometries. We then do a detailed comparison between the more recent
predictions from the lattice regularized theory, and results obtained in the
continuum for the non-trivial ultraviolet fixed point of quantum gravity found
using weak field and non-perturbative methods. In particular we focus on the
derivative of the beta function at the fixed point and the related universal
critical exponent for gravitation. Based on recently available lattice
and continuum results we assess the evidence for the presence of a massless
spin two particle in the continuum limit of the strongly coupled lattice
theory. Finally we compare the lattice prediction for the vacuum-polarization
induced weak scale dependence of the gravitational coupling with recent
calculations in the continuum, finding similar effects.Comment: 46 pages, one figur
Duality Versus Supersymmetry and Compactification
We study the interplay between T-duality, compactification and supersymmetry.
We prove that when the original configuration has unbroken space-time
supersymmetries, the dual configuration also does if a special condition is
met: the Killing spinors of the original configuration have to be independent
on the coordinate which corresponds to the isometry direction of the bosonic
fields used for duality. Examples of ``losers" (T-duals are not supersymmetric)
and ``winners" (T-duals are supersymmetric) are given.Comment: LaTeX file, 19 pages, U. of Groningen Report UG-8/94, Stanford U.
Report SU-ITP-94-19, QMW College Report QMW-PH-94-1