60 research outputs found
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
() which can be thought of as the analogue of the
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 Monte Carlo Simulations of Systems With a Complex Action
We propose a method for Monte Carlo simulations of systems with a complex
action. The method has the advantages of being in principle applicable to any
such system and provides a solution to the overlap problem. In some cases, like
in the IKKT matrix model, a finite size scaling extrapolation can provide
results for systems whose size would make it prohibitive to simulate directly.Comment: Lattice2003(nonzero), 3 pages, 4 figures, Proceedings for Lattice
2003, July 2003, Tsukuba, Japa
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
Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for
We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces
coupled to Ising and three--states Potts model matter. By measuring spin-spin
correlation functions as a function of the geodesic distance we provide
substantial evidence for a diverging correlation length at . The
corresponding scaling exponents are directly related to the KPZ exponents of
the matter fields as conjectured in [4] (NPB454(1995)313).Comment: Talk presented at LATTICE96(gravity
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
Complex zeros of the 2d Ising model on dynamical random lattices
We study the zeros in the complex plane of the partition function for the
Ising model coupled to quantum gravity for complex magnetic field and for
complex temperature. We compute the zeros by using the exact solution coming
from a two matrix model and by Monte Carlo simulations of Ising spins on
dynamical triangulations. We present evidence that the zeros form simple
one-dimensional patterns in the complex plane, and that the critical behaviour
of the system is governed by the scaling of the distribution of singularities
near the critical point.Comment: 3 pages, 8 figures, latex2e, uses espcrc2.sty. Contribution to
Lattice '97, Edinburgh, July 1997, to appear on Nucl. Phys. B (Proc. Suppl.
On the Quantum Geometry of String Theory
The IKKT or IIB matrix model has been proposed as a non-perturbative
definition of type IIB superstring theories. It has the attractive feature that
space--time appears dynamically. It is possible that lower dimensional
universes dominate the theory, therefore providing a dynamical solution to the
reduction of space--time dimensionality. We summarize recent works that show
the central role of the phase of the fermion determinant in the possible
realization of such a scenario.Comment: 3 pages, 2 figures, Lattice2001(surfaces
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
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