553 research outputs found
qQCD and G/G model
The 2D lattice gauge theory with a quantum gauge group is
considered. When , its weak coupling partition
function coincides with the one of the G/G coset model ({\em i.e.} equals the
Verlinde numbers). However, despite such a remarkable coincidence, these models
are not equivalent but, in some certain sense, dual to each other.Comment: 7pp, NBI-HE-93-27, revised. Small changes: several fixed inaccuracies
+ updated reference
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
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
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
Matrix model formulation of four dimensional gravity
The attempt of extending to higher dimensions the matrix model formulation of
two-dimensional quantum gravity leads to the consideration of higher rank
tensor models. We discuss how these models relate to four dimensional quantum
gravity and the precise conditions allowing to associate a four-dimensional
simplicial manifold to Feynman diagrams of a rank-four tensor model.Comment: Lattice 2000 (Gravity), 4 pages,4 figures, uses espcrc2.st
Critical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions
We performed detailed study of the phase transition region in Four
Dimensional Simplicial Quantum Gravity, using the dynamical triangulation
approach. The phase transition between the Gravity and
Antigravity phases turned out to be asymmetrical, so that we observed the
scaling laws only when the Newton constant approached the critical value from
perturbative side. The curvature susceptibility diverges with the scaling index
. The physical (i.e. measured with heavy particle propagation) Hausdorff
dimension of the manifolds, which is
2.3 in the Gravity phase and 4.6 in the Antigravity phase, turned out to be 4
at the critical point, within the measurement accuracy. These facts indicate
the existence of the continuum limit in Four
Dimensional Euclidean Quantum Gravity.Comment: 12pg
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