2,457 research outputs found
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
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
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
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
Twisted Supersymmetric Gauge Theories and Orbifold Lattices
We examine the relation between twisted versions of the extended
supersymmetric gauge theories and supersymmetric orbifold lattices. In
particular, for the SYM in , we show that the continuum
limit of orbifold lattice reproduces the twist introduced by Marcus, and the
examples at lower dimensions are usually Blau-Thompson type. The orbifold
lattice point group symmetry is a subgroup of the twisted Lorentz group, and
the exact supersymmetry of the lattice is indeed the nilpotent scalar
supersymmetry of the twisted versions. We also introduce twisting in terms of
spin groups of finite point subgroups of -symmetry and spacetime symmetry.Comment: 32 page
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
Shape transformations of a model of self-avoiding triangulated surfaces of sphere topology
We study a surface model with a self-avoiding (SA) interaction using the
canonical Monte Carlo simulation technique on fixed-connectivity (FC)
triangulated lattices of sphere topology. The model is defined by an area
energy, a deficit angle energy, and the SA potential. A pressure term is also
included in the Hamiltonian. The volume enclosed by the surface is well defined
because of the self-avoidance. We focus on whether or not the interaction
influences the phase structure of the FC model under two different conditions
of pressure ; zero and small negative. The results are compared
with the previous results of the self-intersecting model, which has a rich
variety of phases; the smooth spherical phase, the tubular phase, the linear
phase, and the collapsed phase. We find that the influence of the SA
interaction on the multitude of phases is almost negligible except for the
evidence that no crumpled surface appears under {\it \Delta} p\=\0 at least
even in the limit of zero bending rigidity \alpha\to \0. The Hausdorff
dimension is obtained in the limit of \alpha\to \0 and compared with previous
results of SA models, which are different from the one in this paper.Comment: 9 figure
Black hole thermodynamics from simulations of lattice Yang-Mills theory
We report on lattice simulations of 16 supercharge SU(N) Yang-Mills quantum
mechanics in the 't Hooft limit. Maldacena duality conjectures that in this
limit the theory is dual to IIA string theory, and in particular that the
behavior of the thermal theory at low temperature is equivalent to that of
certain black holes in IIA supergravity. Our simulations probe the low
temperature regime for N <= 5 and the intermediate and high temperature regimes
for N <= 12. We observe 't Hooft scaling and at low temperatures our results
are consistent with the dual black hole prediction. The intermediate
temperature range is dual to the Horowitz-Polchinski correspondence region, and
our results are consistent with smooth behavior there. We include the Pfaffian
phase arising from the fermions in our calculations where appropriate.Comment: 4 pages, 4 figure
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
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
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