120 research outputs found
Three-dimensional simplicial gravity and combinatorics of group presentations
We demonstrate how some problems arising in simplicial quantum gravity can be
successfully addressed within the framework of combinatorial group theory. In
particular, we argue that the number of simplicial 3-manifolds having a fixed
homology type grows exponentially with the number of tetrahedra they are made
of. We propose a model of 3D gravity interacting with scalar fermions, some
restriction of which gives the 2-dimensional self-avoiding-loop-gas matrix
model. We propose a qualitative picture of the phase structure of 3D simplicial
gravity compatible with the numerical experiments and available analytical
results.Comment: 24 page
Wilson loop on a sphere
We give the formula for a simple Wilson loop on a sphere which is valid for
an arbitrary QCD saddle-point : \mbox{}. The
strong-coupling-phase solution is investigated.Comment: 10 pages, NBI-HE-93-5
Quantum Deformation of Lattice Gauge Theory
A quantum deformation of 3-dimensional lattice gauge theory is defined by
applying the Reshetikhin-Turaev functor to a Heegaard diagram associated to a
given cell complex. In the root-of-unity case, the construction is carried out
with a modular Hopf algebra. In the topological (weak-coupling) limit, the
gauge theory partition function gives a 3-fold invariant, coinciding in the
simplicial case with the Turaev-Viro one. We discuss bounded manifolds as well
as links in manifolds. By a dimensional reduction, we obtain a q-deformed gauge
theory on Riemann surfaces and find a connection with the algebraic
Alekseev-Grosse-Schomerus approach.Comment: 31 pp.; uses epic.sty and eepic.st
3D Gravity and Gauge Theories
I argue that the complete partition function of 3D quantum gravity is given
by a path integral over gauge-inequivalent manifolds times the Chern-Simons
partition function. In a discrete version, it gives a sum over simplicial
complexes weighted with the Turaev-Viro invariant. Then, I discuss how this
invariant can be included in the general framework of lattice gauge theory
(qQCD). To make sense of it, one needs a quantum analog of the Peter-Weyl
theorem and an invariant measure, which are introduced explicitly. The
consideration here is limited to the simplest and most interesting case of
, . At the end, I dwell on 3D generalizations
of matrix models.Comment: 20 pp., NBI-HE-93-67 (Contribution to Proceedings of 1993 Cargese
workshop
Orthogonal polynomial method and odd vertices in matrix models
We show how to use the method of orthogonal polynomials for integrating, in
the planar approximation, the partition function of one-matrix models with a
potential with even or odd vertices, or any combination of them.Comment: 13 pages, 3 Postscript figure
Recursive sampling simulations of 3D gravity coupled to scalar fermions
We study numerically the phase structure of a model of 3D gravity interacting
with scalar fermions. We measure the 3D counterpart of the "string"
susceptibility exponent as a function of the inverse Newton coupling .
We show that there are two phases separated by a critical point around
. The numerical results support the hypothesis that the
phase structures of 3D and 2D simplicial gravity are qualitatively similar, the
inverse Newton coupling in 3D playing the role of the central charge of matter
in 2D.Comment: Latex with 6 figure files, 17 page
The Block Spin Renormalization Group Approach and Two-Dimensional Quantum Gravity
A block spin renormalization group approach is proposed for the dynamical
triangulation formulation of two-dimensional quantum gravity. The idea is to
update link flips on the block lattice in response to link flips on the
original lattice. Just as the connectivity of the original lattice is meant to
be a lattice representation of the metric, the block links are determined in
such a way that the connectivity of the block lattice represents a block
metric. As an illustration, this approach is applied to the Ising model coupled
to two-dimensional quantum gravity. The correct critical coupling is
reproduced, but the critical exponent is obscured by unusually large finite
size effects.Comment: 10 page
- …