Numerical Study of c>1 Matter Coupled to Quantum Gravity

We present the results of a numerical simulation aimed at understanding the nature of the `c = 1 barrier' in two dimensional quantum gravity. We study multiple Ising models living on dynamical $\phi^3$ graphs and analyse the behaviour of moments of the graph loop distribution. We notice a universality at work as the average properties of typical graphs from the ensemble are determined only by the central charge. We further argue that the qualitative nature of these results can be understood from considering the effect of fluctuations about a mean field solution in the Ising sector.Comment: 12 page

TTX-sensitive Na+ and nifedipine-sensitive Ca2+ channels in rat vas deferens smooth muscle cells

The inward currents in single smooth muscle cells (SMC) isolated from epididymal part of rat vas deferens have been studied using whole-cell patch-clamp method. Depolarising steps from holding potential -90 mV evoked inward current with fast and slow components. the component with slow activation possessed voltage-dependent and pharmacological properties characteristic for Ca2+ current carried through L-type calcium channels (I-Ca). the fast component of inward current was activated at around -40 mV, reached its peak at 0 mV, and disappeared upon removal of Na ions from bath solution. This current was blocked in dose-dependent manner by tetrodotoxin (TTX) with an apparent dissociation constant of 6.7 nM. On the basis of voltage-dependent characteristics, TTX sensitivity of fast component of inward current and its disappearance in Na-free solution it is suggested that this current is TTX-sensitive depolarisation activated sodium current (I-Na) Cell dialysis with a pipette solution containing no macroergic compounds resulted in significant inhibition of I-Ca (depression of peak I-Ca by about 81% was observed by 13 min of dialysis), while I-Na remained unaffected during 50 min of dialysis. These data draw first evidence for the existence of TTX-sensitive Na+ current in single SMC isolated from rat vas deferens. These Na+ channels do not appear to be regulated by a phosphorylation process under resting conditions. (C) 1999 Elsevier Science B.V. All rights reserved.Natl Acad Sci Ukraine, Bogomoletz Inst Physiol, Nerve Muscle Physiol Dept, UA-24 Kiev, UkraineUniversidade Federal de São Paulo, Escola Paulista Med, Dept Pharmacol, São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, Dept Pharmacol, São Paulo, BrazilWeb of Scienc

A non-perturbative Lorentzian path integral for gravity

A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated action have a unique Wick rotation to the Euclidean sector. All space-time histories possess a distinguished notion of a discrete proper time. For finite lattice volume, the associated transfer matrix is self-adjoint and bounded. The reflection positivity of the model ensures the existence of a well-defined Hamiltonian. The degenerate geometric phases found previously in dynamically triangulated Euclidean gravity are not present. The phase structure of the new Lorentzian quantum gravity model can be readily investigated by both analytic and numerical methods.Comment: 11 pages, LaTeX, improved discussion of reflection positivity, conclusions unchanged, references update

A second-order phase transition in CDT

Causal Dynamical Triangulations (CDT) are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially be used to define a continuum limit in the conventional sense of nongravitational lattice theories.Comment: 10 pages, 3 figure

Universal Spectral Correlators and Massive Dirac Operators

We derive the large-N spectral correlators of complex matrix ensembles with weights that in the context of Dirac spectra correspond to N_f massive fermions, and prove that the results are universal in the appropriate scaling limits. The resulting microscopic spectral densities satisfy exact spectral sum rules of massive Dirac operators in QCD.Comment: 15 pages, LaTeX. Typographical errors corrected. Note adde