2,324 research outputs found
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
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
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
N=4 Supersymmetry on a Space-Time Lattice
Maximally supersymmetric Yang--Mills theory in four dimensions can be
formulated on a space-time lattice while exactly preserving a single
supersymmetry. Here we explore in detail this lattice theory, paying particular
attention to its strongly coupled regime. Targeting a theory with gauge group
SU(N), the lattice formulation is naturally described in terms of gauge group
U(N). Although the U(1) degrees of freedom decouple in the continuum limit we
show that these degrees of freedom lead to unwanted lattice artifacts at strong
coupling. We demonstrate that these lattice artifacts can be removed, leaving
behind a lattice formulation based on the SU(N) gauge group with the expected
apparently conformal behavior at both weak and strong coupling
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
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
Phase Structure of Lattice N=4 Super Yang-Mills
We make a first study of the phase diagram of four-dimensional N=4 super
Yang-Mills theory regulated on a space-time lattice. The lattice formulation we
employ is both gauge invariant and retains at all lattice spacings one exactly
preserved supersymmetry charge. Our numerical results are consistent with the
existence of a single deconfined phase at all observed values of the bare
coupling.Comment: 29 pages, 11 figures. References added, minor edits to tex
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