96 research outputs found
Monte Carlo Renormalization of 2d Simplicial Quantum Gravity Coupled to Gaussian Matter
We extend a recently proposed real-space renormalization group scheme for
dynamical triangulations to situations where the lattice is coupled to
continuous scalar fields. Using Monte Carlo simulations in combination with a
linear, stochastic blocking scheme for the scalar fields we are able to
determine the leading eigenvalues of the stability matrix with good accuracy
both for c = 1 and c = 10 theories.Comment: 17 pages, 7 figure
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 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
Black hole thermodynamics from simulations of lattice Yang-Mills theory
We report on lattice simulations of 16 supercharge SU(N) Yang-Mills quantum
mechanics in the 't Hooft limit. Maldacena duality conjectures that in this
limit the theory is dual to IIA string theory, and in particular that the
behavior of the thermal theory at low temperature is equivalent to that of
certain black holes in IIA supergravity. Our simulations probe the low
temperature regime for N <= 5 and the intermediate and high temperature regimes
for N <= 12. We observe 't Hooft scaling and at low temperatures our results
are consistent with the dual black hole prediction. The intermediate
temperature range is dual to the Horowitz-Polchinski correspondence region, and
our results are consistent with smooth behavior there. We include the Pfaffian
phase arising from the fermions in our calculations where appropriate.Comment: 4 pages, 4 figure
Non-Perturbative Renormalization Group Flows in Two-Dimensional Quantum Gravity
Recently a block spin renormalization group approach was proposed for the
dynamical triangulation formulation of two-dimensional quantum gravity. We use
this approach to examine non-perturbatively a particular class of higher
derivative actions for pure gravity.Comment: 17 page
First results from simulations of supersymmetric lattices
We conduct the first numerical simulations of lattice theories with exact
supersymmetry arising from the orbifold constructions of
\cite{Cohen:2003xe,Cohen:2003qw,Kaplan:2005ta}. We consider the \cQ=4 theory
in dimensions and the \cQ=16 theory in dimensions. We show
that the U(N) theories do not possess vacua which are stable
non-perturbatively, but that this problem can be circumvented after truncation
to SU(N). We measure the distribution of scalar field eigenvalues, the spectrum
of the fermion operator and the phase of the Pfaffian arising after integration
over the fermions. We monitor supersymmetry breaking effects by measuring a
simple Ward identity. Our results indicate that simulations of
super Yang-Mills may be achievable in the near future.Comment: 25 pages, 14 figures, 9 tables. 3 references adde
Topological gravity on the lattice
In this paper we show that a particular twist of super
Yang-Mills in three dimensions with gauge group SU(2) possesses a set of
classical vacua corresponding to the space of flat connections of the {\it
complexified} gauge group . The theory also contains a set of
topological observables corresponding to Wilson loops wrapping non-trivial
cycles of the base manifold. This moduli space and set of topological
observables is shared with the Chern Simons formulation of three dimensional
gravity and we hence conjecture that the Yang-Mills theory gives an equivalent
description of the gravitational theory. Unlike the Chern Simons formulation
the twisted Yang-Mills theory possesses a supersymmetric and gauge invariant
lattice construction which then provides a possible non-perturbative definition
of three dimensional gravity.Comment: 10 page
A real-space renormalization group for random surfaces
We propose a new real-space renormalization group transformation for dynamical triangulations. It is shown to preserve geometrical exponents such as the string susceptibility and Hausdorff dimension. We furthermore show evidence for a fixed point structure both in pure gravity and gravity coupled to a critical Ising system. In the latter case we are able to extract estimates for the gravitationally dressed exponents which agree to within 2-3% of the KPZ formula
Phase Structure of Dynamical Triangulation Models in Three Dimensions
The dynamical triangulation model of three-dimensional quantum gravity is
shown to have a line of transitions in an expanded phase diagram which includes
a coupling mu to the order of the vertices. Monte Carlo renormalization group
and finite size scaling techniques are used to locate and characterize this
line. Our results indicate that for mu < mu1 ~ -1.0 the model is always in a
crumpled phase independent of the value of the curvature coupling. For mu < 0
the results are in agreement with an approximate mean field treatment. We find
evidence that this line corresponds to first order transitions extending to
positive mu. However, the behavior appears to change for mu > mu2 ~ 2-4. The
simplest scenario that is consistent with the data is the existence of a
critical end point
Minimal Dynamical Triangulations of Random Surfaces
We introduce and investigate numerically a minimal class of dynamical
triangulations of two-dimensional gravity on the sphere in which only vertices
of order five, six or seven are permitted. We show firstly that this
restriction of the local coordination number, or equivalently intrinsic scalar
curvature, leaves intact the fractal structure characteristic of generic
dynamically triangulated random surfaces. Furthermore the Ising model coupled
to minimal two-dimensional gravity still possesses a continuous phase
transition. The critical exponents of this transition correspond to the usual
KPZ exponents associated with coupling a central charge c=1/2 model to
two-dimensional gravity.Comment: Latex, 9 pages, 3 figures, Published versio
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