2,094 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
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
Scaling in Steiner Random Surfaces
It has been suggested that the modified Steiner action functional has
desirable properties for a random surface action. In this paper we investigate
the scaling of the string tension and massgap in a variant of this action on
dynamically triangulated random surfaces and compare the results with the
gaussian plus extrinsic curvature actions that have been used previously.Comment: 7 pages, COLO-HEP-32
Collapsing transition of spherical tethered surfaces with many holes
We investigate a tethered (i.e. fixed connectivity) surface model on
spherical surfaces with many holes by using the canonical Monte Carlo
simulations. Our result in this paper reveals that the model has only a
collapsing transition at finite bending rigidity, where no surface fluctuation
transition can be seen. The first-order collapsing transition separates the
smooth phase from the collapsed phase. Both smooth and collapsed phases are
characterized by Hausdorff dimension H\simeq 2, consequently, the surface
becomes smooth in both phases. The difference between these two phases can be
seen only in the size of surface. This is consistent with the fact that we can
see no surface fluctuation transition at the collapsing transition point. These
two types of transitions are well known to occur at the same transition point
in the conventional surface models defined on the fixed connectivity surfaces
without holes.Comment: 7 pages with 11 figure
In-plane deformation of a triangulated surface model with metric degrees of freedom
Using the canonical Monte Carlo simulation technique, we study a Regge
calculus model on triangulated spherical surfaces. The discrete model is
statistical mechanically defined with the variables , and , which
denote the surface position in , the metric on a two-dimensional
surface and the surface density of , respectively. The metric is
defined only by using the deficit angle of the triangles in {}. This is in
sharp contrast to the conventional Regge calculus model, where {} depends
only on the edge length of the triangles. We find that the discrete model in
this paper undergoes a phase transition between the smooth spherical phase at
and the crumpled phase at , where is the bending
rigidity. The transition is of first-order and identified with the one observed
in the conventional model without the variables and . This implies
that the shape transformation transition is not influenced by the metric
degrees of freedom. It is also found that the model undergoes a continuous
transition of in-plane deformation. This continuous transition is reflected in
almost discontinuous changes of the surface area of and that of ,
where the surface area of is conjugate to the density variable .Comment: 13 pages, 7 figure
Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice
We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have
sign problem in the continuum limit, that is, under the phase-quenched
simulation phase of the determinant localizes to 1 and hence the phase-quench
approximation becomes exact. Among several formulations, we study models by
Cohen-Kaplan-Katz-Unsal (CKKU) and by Sugino. We confirm that the sign problem
is absent in both models and that they converge to the identical continuum
limit without fine tuning. We provide a simple explanation why previous works
by other authors, which claim an existence of the sign problem, do not capture
the continuum physics.Comment: 27 pages, 24 figures; v2: comments and references added; v3: figures
on U(1) mass independence and references added, to appear in JHE
Exact Lattice Supersymmetry: the Two-Dimensional N=2 Wess-Zumino Model
We study the two-dimensional Wess-Zumino model with extended N=2
supersymmetry on the lattice. The lattice prescription we choose has the merit
of preserving {\it exactly} a single supersymmetric invariance at finite
lattice spacing . Furthermore, we construct three other transformations of
the lattice fields under which the variation of the lattice action vanishes to
where is a typical interaction coupling. These four
transformations correspond to the two Majorana supercharges of the continuum
theory. We also derive lattice Ward identities corresponding to these exact and
approximate symmetries. We use dynamical fermion simulations to check the
equality of the massgaps in the boson and fermion sectors and to check the
lattice Ward identities. At least for weak coupling we see no problems
associated with a lack of reflection positivity in the lattice action and find
good agreement with theory. At strong coupling we provide evidence that
problems associated with a lack of reflection positivity are evaded for small
enough lattice spacing.Comment: 29 pages, 10 figures. New results at strong coupling added. Minor
corrections to text and one reference added. Version to appear in Phys. Rev.
Phase transitions of a tethered surface model with a deficit angle term
Nambu-Goto model is investigated by using the canonical Monte Carlo
simulations on fixed connectivity surfaces of spherical topology. Three
distinct phases are found: crumpled, tubular, and smooth. The crumpled and the
tubular phases are smoothly connected, and the tubular and the smooth phases
are connected by a discontinuous transition. The surface in the tubular phase
forms an oblong and one-dimensional object similar to a one-dimensional linear
subspace in the Euclidean three-dimensional space R^3. This indicates that the
rotational symmetry inherent in the model is spontaneously broken in the
tubular phase, and it is restored in the smooth and the crumpled phases.Comment: 6 pages with 6 figure
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