398 research outputs found
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
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
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
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
Supersymmetric Deformations of Type IIB Matrix Model as Matrix Regularization of N=4 SYM
We construct a supersymmetry and global symmetry
preserving deformation of the type IIB matrix model. This model, without
orbifold projection, serves as a nonperturbative regularization for
supersymmetric Yang-Mills theory in four Euclidean dimensions.
Upon deformation, the eigenvalues of the bosonic matrices are forced to reside
on the surface of a hypertorus. We explicitly show the relation between the
noncommutative moduli space of the deformed matrix theory and the Brillouin
zone of the emergent lattice theory. This observation makes the transmutation
of the moduli space into the base space of target field theory clearer. The
lattice theory is slightly nonlocal, however the nonlocality is suppressed by
the lattice spacing. In the classical continuum limit, we recover the
SYM theory. We also discuss the result in terms of D-branes and
interpret it as collective excitations of D(-1) branes forming D3 branes.Comment: Version 2: Extended discussion of moduli space, added a referenc
Matrix Models, Monopoles and Modified Moduli
Motivated by the Dijkgraaf-Vafa correspondence, we consider the matrix model
duals of N=1 supersymmetric SU(Nc) gauge theories with Nf flavors. We
demonstrate via the matrix model solutions a relation between vacua of theories
with different numbers of colors and flavors. This relation is due to an N=2
nonrenormalization theorem which is inherited by these N=1 theories.
Specializing to the case Nf=Nc, the simplest theory containing baryons, we
demonstrate that the explicit matrix model predictions for the locations on the
Coulomb branch at which monopoles condense are consistent with the quantum
modified constraints on the moduli in the theory. The matrix model solutions
include the case that baryons obtain vacuum expectation values. In specific
cases we check explicitly that these results are also consistent with the
factorization of corresponding Seiberg-Witten curves. Certain results are
easily understood in terms of M5-brane constructions of these gauge theories.Comment: 27 pages, LaTeX, 2 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
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
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