New multicritical matrix models and multicritical 2d CDT

We define multicritical CDT models of 2d quantum gravity and show that they are a special case of multicritical generalized CDT models obtained from the new scaling limit, the so-called "classical" scaling limit, of matrix models. The multicritical behavior agrees with the multicritical behavior of the so-called branched polymers.Comment: 16 pages, 4 figures. References adde

A statistical formalism of Causal Dynamical Triangulations

We rewrite the 1+1 Causal Dynamical Triangulations model as a spin system and thus provide a new method of solution of the model.Comment: 21 pages, 19 pictures, 1 graph, Published in section: Field Theory And Statistical System

Barriers in Quantum Gravity

I discuss recent progress in our understanding of two barriers in quantum gravity: $c > 1$ in the case of 2d quantum gravity and $D > 2$ in the case of Euclidean Einstein-Hilbert gravity formulated in space-time dimensions $D >2$.Comment: standard latex, 10 pages. (one year old contribution to Trieste workshop, but continued demand for preprints has motivated me to put it on the bulletin board), NBI-HE-93-3

Topology and Confinement in SU(N) Gauge Theories

The large N limit of SU(N) gauge theories in 3+1 dimensions is investigated on the lattice by extrapolating results obtained for $2 \le N \le 5$. A numerical determination of the masses of the lowest-lying glueball states and of the topological susceptibility in the limit $N\to\infty$ is provided. Ratios of the tensions of stable k-strings over the tension of the fundamental string are investigated in various regimes and the results are compared with expectations based on several scenarios -- in particular MQCD and Casimir scaling. While not conclusive at zero temperature in D=3+1, in the other cases investigated our data seem to favour the latter.Comment: 3 pages, 2 figures; talk presented by B. Lucini at Lattice2001(confinement

Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ``dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian- and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde

Scaling with a modified Wilson action which suppresses Z_2 artifacts in SU(2) lattice gauge theories

A modified Wilson action which suppresses plaquettes which take negative values is used to study the scaling behavior of the string tension. The use of the \b_E scheme gives good agreement with asymptotic two loop results.Comment: Latex (ps figure appended in the end), 7 page

Center Disorder in the 3D Georgi-Glashow Model

We present a number of arguments relating magnetic disorder to center disorder, in pure Yang-Mills theory in D=3 and D=4 dimensions. In the case of the D=3 Georgi-Glashow model, we point out that the abelian field distribution is not adequatedly represented, at very large scales, by that of a monopole Coulomb gas. The onset of center disorder is associated with the breakdown of the Coulomb gas approximation; this scale is pushed off to infinity in the QED_3 limit of the 3D Georgi-Glashow model, but should approach the color-screening length in the pure Yang-Mills limit.Comment: 22 pages including 3 figures, Latex2

A model for emergence of space and time

We study string field theory (third quantization) of the two-dimensional model of quantum geometry called generalized CDT ("causal dynamical triangulations"). Like in standard non-critical string theory the so-called string field Hamiltonian of generalized CDT can be associated with W-algebra generators through the string mode expansion. This allows us to define an "absolute" vacuum. "Physical" vacua appear as coherent states created by vertex operators acting on the absolute vacuum. Each coherent state corresponds to specific values of the coupling constants of generalized CDT. The cosmological "time" only exists relatively to a given "physical" vacuum and comes into existence before space, which is created because the "physical" vacuum is unstable. Thus each CDT "universe" is created as a "Big Bang" from the absolute vacuum, its time evolution is governed by the CDT string field Hamiltonian with given coupling constants, and one can imagine interactions between CDT universes with different coupling constants ("fourth quantization"

Scattering amplitudes of regularized bosonic strings

We compute scattering amplitudes of the regularized bosonic Nambu-Goto string in the mean-field approximation, disregarding fluctuations of the Lagrange multiplier and an independent metric about their mean values. We use the previously introduced Lilliputian scaling limit to recover the Regge behavior of the amplitudes with the usual linear Regge trajectory in space-time dimensions d>2. We demonstrate a stability of this minimum of the effective action under fluctuations for d<26.Comment: 11 pages, v2: typos corrected, to appear in PR