where
denotes the SU(2)-holonomy around
b
and
is proportional to the inverse square coupling constant,
. One motivation was to understand whether in the well-defined
pure-gravity region, one can choose the elementary particle
masses to be
as
, as one might expect for a realistic gravity+matter system.
This seems a rather distant hope, since in the simulations
performed so far, the ratio
is of order unity.
Initial computations were performed on a
-lattice with the scale-invariant measure, and at
k
=0.01 [42,
44], and extended to larger
k
-values in [43]. For
, one finds some evidence for a (first-order?) transition; the
region of
where the transition occurs does not change much with
k
. Beirl et al [27,
28] extended this analysis by measuring the static potential
V
of a quark-antiquark pair on lattices of size
and
. With and without gravity, one finds both a confined and a
deconfined phase; in the presence of gravity, the transition
occurs at a smaller
-value. More recently, Berg et al [41] have gathered further data on the location and stability of the
well-defined phase in the
-plane, and extracted a string tension for various
-values.
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Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll http://www.livingreviews.org/lrr-1998-13 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |