1,718 research outputs found
Thermal phases of D1-branes on a circle from lattice super Yang-Mills
We report on the results of numerical simulations of 1+1 dimensional SU(N)
Yang-Mills theory with maximal supersymmetry at finite temperature and
compactified on a circle. For large N this system is thought to provide a dual
description of the decoupling limit of N coincident D1-branes on a circle. It
has been proposed that at large N there is a phase transition at strong
coupling related to the Gregory-Laflamme (GL) phase transition in the
holographic gravity dual. In a high temperature limit there was argued to be a
deconfinement transition associated to the spatial Polyakov loop, and it has
been proposed that this is the continuation of the strong coupling GL
transition. Investigating the theory on the lattice for SU(3) and SU(4) and
studying the time and space Polyakov loops we find evidence supporting this. In
particular at strong coupling we see the transition has the parametric
dependence on coupling predicted by gravity. We estimate the GL phase
transition temperature from the lattice data which, interestingly, is not yet
known directly in the gravity dual. Fine tuning in the lattice theory is
avoided by the use of a lattice action with exact supersymmetry.Comment: 21 pages, 8 figures. v2: References added, two figures were modified
for clarity. v3: Normalisation of lattice coupling corrected by factor of two
resulting in change of estimate for c_cri
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
Relations among Supersymmetric Lattice Gauge Theories via Orbifolding
We show how to derive Catterall's supersymmetric lattice gauge theories
directly from the general principle of orbifolding followed by a variant of the
usual deconstruction. These theories are forced to be complexified due to a
clash between charge assignments under U(1)-symmetries and lattice assignments
in terms of scalar, vector and tensor components for the fermions. Other
prescriptions for how to discretize the theory follow automatically by
orbifolding and deconstruction. We find that Catterall's complexified model for
the two-dimensional N=(2,2) theory has two independent preserved
supersymmetries. We comment on consistent truncations to lattice theories
without this complexification and with the correct continuum limit. The
construction of lattice theories this way is general, and can be used to derive
new supersymmetric lattice theories through the orbifolding procedure. As an
example, we apply the prescription to topologically twisted four-dimensional
N=2 supersymmetric Yang-Mills theory. We show that a consistent truncation is
closely related to the lattice formulation previously given by Sugino.Comment: 20 pages, LaTeX2e, no figur
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
Towards lattice simulation of the gauge theory duals to black holes and hot strings
A generalization of the AdS/CFT conjecture postulates a duality between IIA
string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't
Hooft limit. At low temperatures string theory describes black holes, whose
thermodynamics may hence be studied using the dual quantum mechanics. This
quantum mechanics is strongly coupled which motivates the use of lattice
techniques. We argue that, contrary to expectation, the theory when discretized
naively will nevertheless recover continuum supersymmetry as the lattice
spacing is sent to zero. We test these ideas by studying the 4 supercharge
version of this Yang-Mills quantum mechanics in the 't Hooft limit. We use both
a naive lattice action and a manifestly supersymmetric action. Using Monte
Carlo methods we simulate the Euclidean theories, and study the lattice
continuum limit, for both thermal and non-thermal periodic boundary conditions,
confirming continuum supersymmetry is recovered for the naive action when
appropriate. We obtain results for the thermal system with N up to 12. These
favor the existence of a single deconfined phase for all non-zero temperatures.
These results are an encouraging indication that the 16 supercharge theory is
within reach using similar methods and resources.Comment: 49 pages, 14 figure
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
A lattice study of the two-dimensional Wess Zumino model
We present results from a numerical simulation of the two-dimensional
Euclidean Wess-Zumino model. In the continuum the theory possesses N=1
supersymmetry. The lattice model we employ was analyzed by Golterman and
Petcher in \cite{susy} where a perturbative proof was given that the continuum
supersymmetric Ward identities are recovered without finite tuning in the limit
of vanishing lattice spacing. Our simulations demonstrate the existence of
important non-perturbative effects in finite volumes which modify these
conclusions. It appears that in certain regions of parameter space the vacuum
state can contain solitons corresponding to field configurations which
interpolate between different classical vacua. In the background of these
solitons supersymmetry is partially broken and a light fermion mode is
observed. At fixed coupling the critical mass separating phases of broken and
unbroken supersymmetry appears to be volume dependent. We discuss the
implications of our results for continuum supersymmetry breaking.Comment: 32 pages, 12 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
Two-dimensional N=(2,2) super Yang-Mills theory on computer
We carry out preliminary numerical study of Sugino's lattice formulation
\cite{Sugino:2004qd,Sugino:2004qdf} of the two-dimensional
super Yang-Mills theory (2d SYM) with the gauge group
\SU(2). The effect of dynamical fermions is included by re-weighting a
quenched ensemble by the pfaffian factor. It appears that the complex phase of
the pfaffian due to lattice artifacts and flat directions of the classical
potential are not problematic in Monte Carlo simulation. Various one-point
supersymmetric Ward-Takahashi (WT) identities are examined for lattice spacings
up to with the fixed physical lattice size , where
denotes the gauge coupling constant in two dimensions. WT identities implied by
an exact fermionic symmetry of the formulation are confirmed in fair accuracy
and, for most of these identities, the quantum effect of dynamical fermions is
clearly observed. For WT identities expected only in the continuum limit, the
results seem to be consistent with the behavior expected from supersymmetry,
although we do not see clear distintion from the quenched simulation. We
measure also the expectation values of renormalized gauge-invariant bi-linear
operators of scalar fields.Comment: 24 pages, 10 figures, the distribution of the complex phase of the
pffafian is also measured, the final version to appear in JHE
Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group
We propose a lattice model for two-dimensional SU(N) N=(2,2) super Yang-Mills
model. We start from the CKKU model for this system, which is valid only for
U(N) gauge group. We give a reduction of U(1) part keeping a part of
supersymmetry. In order to suppress artifact vacua, we use an admissibility
condition.Comment: 16 pages, 3 figures; v2: typo crrected; v3: 18 pages, a version to
appear in JHE
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