1,857 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
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
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
Three Dimensional N=2 Supersymmetry on the Lattice
We show how 3-dimensional, N=2 supersymmetric theories, including super QCD
with matter fields, can be put on the lattice with existing techniques, in a
way which will recover supersymmetry in the small lattice spacing limit.
Residual supersymmetry breaking effects are suppressed in the small lattice
spacing limit by at least one power of the lattice spacing a.Comment: 21 pages, 2 figures, typo corrected, reference adde
On the Isomorphic Description of Chiral Symmetry Breaking by Non-Unitary Lie Groups
It is well-known that chiral symmetry breaking (SB) in QCD with
light quark flavours can be described by orthogonal groups as , due to local isomorphisms. Here we discuss the question how specific
this property is. We consider generalised forms of SB involving an
arbitrary number of light flavours of continuum or lattice fermions, in various
representations. We search systematically for isomorphic descriptions by
non-unitary, compact Lie groups. It turns out that there are a few alternative
options in terms of orthogonal groups, while we did not find any description
entirely based on symplectic or exceptional Lie groups. If we adapt such an
alternative as the symmetry breaking pattern for a generalised Higgs mechanism,
we may consider a Higgs particle composed of bound fermions and trace back the
mass generation to SB. In fact, some of the patterns that we encounter
appear in technicolour models. In particular if one observes a Higgs mechanism
that can be expressed in terms of orthogonal groups, we specify in which cases
it could also represent some kind of SB of techniquarks.Comment: 18 pages, to appear in Int. J. Mod. Phys.
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
Smooth Random Surfaces from Tight Immersions?
We investigate actions for dynamically triangulated random surfaces that
consist of a gaussian or area term plus the {\it modulus} of the gaussian
curvature and compare their behavior with both gaussian plus extrinsic
curvature and ``Steiner'' actions.Comment: 7 page
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