On the phase diagram of 2d Lorentzian Quantum Gravity

The phase diagram of 2d Lorentzian quantum gravity (LQG) coupled to conformal matter is studied. A phase transition is observed at $c=c_{\rm crit}$ ($1/2<c_{\rm crit}<4$) which can be thought of as the analogue of the $c=1$ barrier of Euclidean quantum gravity (EQG). The non--trivial properties of the quantum geometry are discussed.Comment: LATTICE99(gravity), 3 pages, espcrc2.sty, simulations available at http://www.nbi.dk/~ambjorn/lqg2

Making the gravitational path integral more Lorentzian, or: Life beyond Liouville gravity

In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a number of appealing features: i) its quantum geometry is non-fractal, ii) it remains consistent when coupled to matter, even beyond the c=1 barrier, iii) it is closer to canonical quantization approaches than previous path-integral formulations, and iv) its construction generalizes to higher dimensions.Comment: 4 pages, 2 figures (postscript), uses espcrc2.st

The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-

Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method can be applied to any system with a complex action, and it eliminates the so-called overlap problem completely. We test the new approach in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density. The achieved system size is large enough to extract the thermodynamic limit. Our results provide a clear understanding of how the expected first order phase transition is induced by the imaginary part of the action.Comment: 27 pages, 25 figure

The Quantum Spacetime of c>0 2d Gravity

We review recent developments in the understanding of the fractal properties of quantum spacetime of 2d gravity coupled to c>0 conformal matter. In particular we discuss bounds put by numerical simulations using dynamical triangulations on the value of the Hausdorff dimension d_H obtained from scaling properties of two point functions defined in terms of geodesic distance. Further insight to the fractal structure of spacetime is obtained from the study of the loop length distribution function which reveals that the 0<c<= 1 system has similar geometric properties with pure gravity, whereas the branched polymer structure becomes clear for c >= 5.Comment: LaTeX2e, 3 pages, 3 figure

Representation of SU(infinity) Algebra for Matrix Models

We investigate how the matrix representation of SU(N) algebra approaches that of the Poisson algebra in the large N limit. In the adjoint representation, the (N^2-1) times (N^2-1) matrices of the SU(N) generators go to those of the Poisson algebra in the large N limit. However, it is not the case for the N times N matrices in the fundamental representation.Comment: 8 page

Simulating Simplified Versions of the IKKT Matrix Model

We simulate a supersymmetric matrix model obtained from dimensional reduction of 4d SU(N) super Yang-Mills theory (a 4d counter part of the IKKT model or IIB matrix model). The eigenvalue distribution determines the space structure. The measurement of Wilson loop correlators reveals a universal large N scaling. Eguchi-Kawai equivalence may hold in a finite range of scale, which is also true for the bosonic case. We finally report on simulations of a low energy approximation of the 10d IKKT model, where we omit the phase of the Pfaffian and look for evidence for a spontaneous Lorentz symmetry breaking.Comment: 4 pages, talk presented at LATTICE 2000 (Bangalore

Gauged Fermionic Q-balls

We present a new model for a non-topological soliton (NTS) that contains interacting fermions, scalar particles and a gauge field. Using a variational approach, we estimate the energy of the localized configuration, showing that it can be the lowest energy state of the system for a wide range of parameters.Comment: 5 pages, 2 figures; revised version to appear in Phys. Rev.

Phase structure of twisted Eguchi-Kawai model

We study the phase structure of the four-dimensional twisted Eguchi-Kawai model using numerical simulations. This model is an effective tool for studying SU(N) gauge theory in the large-N limit and provides a nonperturbative formulation of the gauge theory on noncommutative spaces. Recently it was found that its Z_N^4 symmetry, which is crucial for the validity of this model, can break spontaneously in the intermediate coupling region. We investigate in detail the symmetry breaking point from the weak coupling side. Our simulation results show that the continuum limit of this model cannot be taken.Comment: 7 pages, 4 figures, talk presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4, 2007, Regensburg, German

Gauged Dimension Bubbles

Some of the peculiar electrodynamical effects associated with gauged ``dimension bubbles'' are presented. Such bubbles, which effectively enclose a region of 5d spacetime, can arise from a 5d theory with a compact extra dimension. Bubbles with thin domain walls can be stabilized against total collapse by the entrapment of light charged scalar bosons inside the bubble, extending the idea of a neutral dimension bubble to accommodate the case of a gauged U(1) symmetry. Using a dielectric approach to the 4d dilaton-Maxwell theory, it is seen that the bubble wall is almost totally opaque to photons, leading to a new stabilization mechanism due to trapped photons. Photon dominated bubbles very slowly shrink, resulting in a temperature increase inside the bubble. At some critical temperature, however, these bubbles explode, with a release of radiation.Comment: 14 pages, no figures; to appear in Phys.Rev.