2,135 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
The Flat Phase of Crystalline Membranes
We present the results of a high-statistics Monte Carlo simulation of a
phantom crystalline (fixed-connectivity) membrane with free boundary. We verify
the existence of a flat phase by examining lattices of size up to . The
Hamiltonian of the model is the sum of a simple spring pair potential, with no
hard-core repulsion, and bending energy. The only free parameter is the the
bending rigidity . In-plane elastic constants are not explicitly
introduced. We obtain the remarkable result that this simple model dynamically
generates the elastic constants required to stabilise the flat phase. We
present measurements of the size (Flory) exponent and the roughness
exponent . We also determine the critical exponents and
describing the scale dependence of the bending rigidity () and the induced elastic constants (). At bending rigidity , we find
(Hausdorff dimension ), and . These results are consistent with the scaling relation . The additional scaling relation implies
. A direct measurement of from the power-law decay of
the normal-normal correlation function yields on the
lattice.Comment: Latex, 31 Pages with 14 figures. Improved introduction, appendix A
and discussion of numerical methods. Some references added. Revised version
to appear in J. Phys.
Matrix formulation of superspace on 1D lattice with two supercharges
Following the approach developed by some of the authors in recent papers and
using a matrix representation for the superfields, we formulate an exact
supersymmetric theory with two supercharges on a one dimensional lattice. In
the superfield formalism supersymmetry transformations are uniquely defined and
do not suffer of the ambiguities recently pointed out by some authors. The
action can be written in a unique way and it is invariant under all
supercharges. A modified Leibniz rule applies when supercharges act on a
superfield product and the corresponding Ward identities take a modified form
but hold exactly at least at the tree level, while their validity in presence
of radiative corrections is still an open problem and is not considered here.Comment: 25 page
Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry
A manifestly supersymmetric nonperturbative matrix regularization for a
twisted version of N=(8,8) theory on a curved background (a two-sphere) is
constructed. Both continuum and the matrix regularization respect four exact
scalar supersymmetries under a twisted version of the supersymmetry algebra. We
then discuss a succinct Q=1 deformed matrix model regularization of N=4 SYM in
d=4, which is equivalent to a non-commutative orbifold lattice
formulation. Motivated by recent progress in supersymmetric lattices, we also
propose a N=1/4 supersymmetry preserving deformation of N=4 SYM theory on
. In this class of N=1/4 theories, both the regularized and continuum
theory respect the same set of (scalar) supersymmetry. By using the equivalence
of the deformed matrix models with the lattice formulations, we give a very
simple physical argument on why the exact lattice supersymmetry must be a
subset of scalar subalgebra. This argument disagrees with the recent claims of
the link approach, for which we give a new interpretation.Comment: 47 pages, 3 figure
Exact Vacuum Energy of Orbifold Lattice Theories
We investigate the orbifold lattice theories constructed from supersymmetric
Yang-Mills matrix theories (mother theories) with four and eight supercharges.
We show that the vacuum energy of these theories does not receive any quantum
correction perturbatively.Comment: 14 pages, no figure, LaTeX2e, typos corrected, errors in references
corrected, comments adde
A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
We construct super Yang-Mills theories with extended supersymmetry on
hypercubic lattices of various dimensions keeping one or two supercharges
exactly. Gauge fields are represented by ordinary unitary link variables, and
the exact supercharges are nilpotent up to gauge transformations. Among the
models, we show that the desired continuum theories are obtained without any
fine tuning of parameters for the cases in two-dimensions.Comment: 29 pages, 1 figure, LaTeX, (v2) problem on degenerate vacua
discussed, renormalization arguments modified, (v3) explanations and
references added, published version in JHE
Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice
We continue to construct lattice super Yang-Mills theories along the line
discussed in the previous papers \cite{sugino, sugino2}. In our construction of
theories in four dimensions, the problem of degenerate vacua
seen in \cite{sugino} is resolved by extending some fields and soaking up
would-be zero-modes in the continuum limit, while in the weak coupling
expansion some surplus modes appear both in bosonic and fermionic sectors
reflecting the exact supersymmetry. A slight modification to the models is made
such that all the surplus modes are eliminated in two- and three-dimensional
models obtained by dimensional reduction thereof. models in
three dimensions need fine-tuning of three and one parameters respectively to
obtain the desired continuum theories, while two-dimensional models with do not require any fine-tuning.Comment: 28 pages, no figure, LaTeX, JHEP style; (v2) published version to
JHEP; (v3) argument on the vacuum degeneracy revised, 34 page
Lattice supersymmetry, superfields and renormalization
We study Euclidean lattice formulations of non-gauge supersymmetric models
with up to four supercharges in various dimensions. We formulate the conditions
under which the interacting lattice theory can exactly preserve one or more
nilpotent anticommuting supersymmetries. We introduce a superfield formalism,
which allows the enumeration of all possible lattice supersymmetry invariants.
We use it to discuss the formulation of Q-exact lattice actions and their
renormalization in a general manner. In some examples, one exact supersymmetry
guarantees finiteness of the continuum limit of the lattice theory. As a
consequence, we show that the desired quantum continuum limit is obtained
without fine tuning for these models. Finally, we discuss the implications and
possible further applications of our results to the study of gauge and
non-gauge models.Comment: 44 pages, 1 figur
Technicolor and Beyond: Unification in Theory Space
The salient features of models of dynamical electroweak symmetry breaking are
reviewed. The ideal walking idea is introduced according to which one should
carefully take into account the effects of the extended technicolor dynamics on
the technicolor dynamics itself. The effects amount at the enhancement of the
anomalous dimension of the mass of the techniquarks allowing to decouple the
Flavor Changing Neutral Currents problem from the one of the generation of the
top mass. Precision data constraints are reviewed focussing on the latest
crucial observation that the S-parameter can be computed exactly near the upper
end of the conformal window (Conformal S-parameter) with relevant consequences
on the selection of nature's next strong force. We will then introduce the
Minimal Walking Technicolor (MWT) models. In the second part of this review we
consider the interesting possibility to marry supersymmetry and technicolor.
The reason is to provide a unification of different extensions of the standard
model. For example, this means that one can recover, according to the
parameters and spectrum of the theory distinct extensions of the standard
model, from supersymmetry to technicolor and unparticle physiscs. A surprising
result is that a minimal (in terms of the smallest number of fields)
supersymmetrization of the MWT model leads to the maximal supersymmetry in four
dimensions, i.e. N=4 SYM.Comment: Extended version of the PASCOS10 proceedings for the Plenary Tal
First Results from Lattice Simulation of the PWMM
We present results of lattice simulations of the Plane Wave Matrix Model
(PWMM). The PWMM is a theory of supersymmetric quantum mechanics that has a
well-defined canonical ensemble. We simulate this theory by applying rational
hybrid Monte Carlo techniques to a naive lattice action. We examine the strong
coupling behaviour of the model focussing on the deconfinement transition.Comment: v3 20 pages, 8 figures, comment adde
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