3,076 research outputs found
Singular Vertices and the Triangulation Space of the D-sphere
By a sequence of numerical experiments we demonstrate that generic
triangulations of the sphere for contain one {\it singular}
simplex. The mean number of elementary simplices sharing this
simplex increases with the volume of the triangulation according to a simple
power law. The lower dimension subsimplices associated with this
simplex also show a singular behaviour. Possible consequences for the
DT model of four-dimensional quantum gravity are discussed.Comment: 15 pages, 9 figure
Lattice formulation of (2,2) supersymmetric gauge theories with matter fields
We construct lattice actions for a variety of (2,2) supersymmetric gauge
theories in two dimensions with matter fields interacting via a superpotential.Comment: 13 pages, 2 figures. Appendix added, references updated, typos fixe
A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
We propose a discretization of two dimensional Euclidean Yang-Mills theories
with N=2 supersymmetry which preserves exactly both gauge invariance and an
element of supersymmetry. The approach starts from the twisted form of the
continuum super Yang Mills action which we show may be written in terms of two
real Kahler-Dirac fields whose components transform into each other under the
twisted supersymmetry. Once the theory is written in this geometrical language
it is straightforward to discretize by mapping the component tensor fields to
appropriate geometrical structures in the lattice and by replacing the
continuum exterior derivative and its adjoint by appropriate lattice covariant
difference operators. The lattice action is local and possesses a unique vacuum
state while the use of Kahler-Dirac fermions ensures the model does not exhibit
spectrum doubling.Comment: Minor typos fixed. Version to be published in JHE
Simulating Four-Dimensional Simplicial Gravity using Degenerate Triangulations
We extend a model of four-dimensional simplicial quantum gravity to include
degenerate triangulations in addition to combinatorial triangulations
traditionally used. Relaxing the constraint that every 4-simplex is uniquely
defined by a set of five distinct vertexes, we allow triangulations containing
multiply connected simplexes and distinct simplexes defined by the same set of
vertexes. We demonstrate numerically that including degenerated triangulations
substantially reduces the finite-size effects in the model. In particular, we
provide a strong numerical evidence for an exponential bound on the entropic
growth of the ensemble of degenerate triangulations, and show that a
discontinuous crumpling transition is already observed on triangulations of
volume N_4 ~= 4000.Comment: Latex, 8 pages, 4 eps-figure
Baby Universes in 4d Dynamical Triangulation
We measure numerically the distribution of baby universes in the crumpled
phase of the dynamical triangulation model of 4d quantum gravity. The relevance
of the results to the issue of an exponential bound is discussed. The data are
consistent with the existence of such a bound.Comment: 8 pages, 4 figure
Deconstruction and other approaches to supersymmetric lattice field theories
This report contains both a review of recent approaches to supersymmetric
lattice field theories and some new results on the deconstruction approach. The
essential reason for the complex phase problem of the fermion determinant is
shown to be derivative interactions that are not present in the continuum.
These irrelevant operators violate the self-conjugacy of the fermion action
that is present in the continuum. It is explained why this complex phase
problem does not disappear in the continuum limit. The fermion determinant
suppression of various branches of the classical moduli space is explored, and
found to be supportive of previous claims regarding the continuum limit.Comment: 70 page
Wess-Zumino model with exact supersymmetry on the lattice
A lattice formulation of the four dimensional Wess-Zumino model that uses
Ginsparg-Wilson fermions and keeps exact supersymmetry is presented. The
supersymmetry transformation that leaves invariant the action at finite lattice
spacing is determined by performing an iterative procedure in the coupling
constant. The closure of the algebra, generated by this transformation is also
showed.Comment: 13 pages. Few references added. New appendix on Ward identity added.
Version to be published in JHE
Simplicial Gravity in Dimension Greater than Two
We consider two issues in the DT model of quantum gravity. First, it is shown
that the triangulation space for D>3 is dominated by triangulations containing
a single singular (D-3)-simplex composed of vertices with divergent dual
volumes. Second we study the ergodicity of current simulation algorithms.
Results from runs conducted close to the phase transition of the
four-dimensional theory are shown. We see no strong indications of ergodicity
br eaking in the simulation and our data support recent claims that the
transition is most probably first order. Furthermore, we show that the critical
properties of the system are determined by the dynamics of remnant singular
vertices.Comment: Talk presented at LATTICE96(gravity
Singular Structure in 4D Simplicial Gravity
We show that the phase transition previously observed in dynamical
triangulation models of quantum gravity can be understood as being due to the
creation of a singular link. The transition between singular and non-singular
geometries as the gravitational coupling is varied appears to be first order.Comment: 9 pages, 5 figures, 3 references adde
Lattice formulation of super Yang-Mills theory
We construct a lattice action for super Yang-Mills theory in
four dimensions which is local, gauge invariant, free of spectrum doubling and
possesses a single exact supersymmetry. Our construction starts from the
observation that the fermions of the continuum theory can be mapped into the
component fields of a single real anticommuting Kahler-Dirac field. The
original supersymmetry algebra then implies the existence of a nilpotent scalar
supercharge and a corresponding set of bosonic superpartners. Using this
field content we write down a -exact action and show that, with an
appropriate change of variables, it reduces to a well-known twist of super Yang-Mills theory due to Marcus. Using the discretization
prescription developed in an earlier paper on the theory in two
dimensions we are able to translate this geometrical action to the lattice.Comment: 15 pages. 1 reference correcte
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