2,808 research outputs found
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
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
Testing a Fourier Accelerated Hybrid Monte Carlo Algorithm
We describe a Fourier Accelerated Hybrid Monte Carlo algorithm suitable for
dynamical fermion simulations of non-gauge models. We test the algorithm in
supersymmetric quantum mechanics viewed as a one-dimensional Euclidean lattice
field theory. We find dramatic reductions in the autocorrelation time of the
algorithm in comparison to standard HMC.Comment: 9 pages, 3 figure
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
A Critique of the Link Approach to Exact Lattice Supersymmetry
We examine the link approach to constructing a lattice theory of N=2 super
Yang Mills theory in two dimensions. The goal of this construction is to
provide a discretization of the continuum theory which preserves all
supersymmetries at non-zero lattice spacing. We show that this approach suffers
from an inconsistency and argue that a maximum of just one of the
supersymmetries can be implemented on the lattice.Comment: 7 page
Exact Ward-Takahashi identity for the lattice N=1 Wess-Zumino model
The lattice Wess-Zumino model written in terms of the Ginsparg-Wilson
relation is invariant under a generalized supersymmetry transformation which is
determined by an iterative procedure in the coupling constant. By studying the
associated Ward-Takahashi identity up to order we show that this lattice
supersymmetry automatically leads to restoration of continuum supersymmetry
without fine tuning. In particular, the scalar and fermion renormalization wave
functions coincide.Comment: 6 pages, 5 figures, Talk given at QG05, Cala Gonone, Sardinia, Italy.
12-16 September 200
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
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
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
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