55 research outputs found
Lattice supersymmetry in 1D with two supercharges
A consistent formulation of a fully supersymmetric theory on the lattice has
been a long standing challenge. In recent years there has been a renewed
interest on this problem with different approaches. At the basis of the
formulation we present in the following there is the Dirac-Kahler twisting
procedure, which was proposed in the continuum for a number of theories,
including N=4 SUSY in four dimensions. Following the formalism developed in
recent papers, an exact supersymmetric theory with two supercharges on a one
dimensional lattice is realized using a matrix-based model. The matrix
structure is obtained from the shift and clock matrices used in two dimensional
non-commutative field theories. The matrix structure reproduces on a one
dimensional lattice the expected modified Leibniz rule. Recent claims of
inconsistency of the formalism are discussed and shown not to be relevant.Comment: 14 pages, Presented by SA and AD at the XXV International Symposium
on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German
Power grids vulnerability: a complex network approach
Power grids exhibit patterns of reaction to outages similar to complex
networks. Blackout sequences follow power laws, as complex systems operating
near a critical point. Here, the tolerance of electric power grids to both
accidental and malicious outages is analyzed in the framework of complex
network theory. In particular, the quantity known as efficiency is modified by
introducing a new concept of distance between nodes. As a result, a new
parameter called net-ability is proposed to evaluate the performance of power
grids. A comparison between efficiency and net-ability is provided by
estimating the vulnerability of sample networks, in terms of both the metrics.Comment: 16 pages, 3 figures. Figure 2 and table II modified. Typos corrected.
Version accepted for publication in Chao
Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice
We propose a twisted SUSY invariant formulation of Chern-Simons theory on a
Euclidean three dimensional lattice. The SUSY algebra to be realized on the
lattice is the N=4 D=3 twisted algebra that was recently proposed by D'Adda et
al.. In order to keep the manifest anti-hermiticity of the action, we introduce
oppositely oriented supercharges. Accordingly, the naive continuum limit of the
action formally corresponds to the Landau gauge fixed version of Chern-Simons
theory with complex gauge group which was originally proposed by Witten. We
also show that the resulting action consists of parity even and odd parts with
different coefficients.Comment: 22 pages, 5 figures; v2,v3 added references, v4 added two paragraphs
and one figure in the summar
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
Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
The lattice superalgebra of the link approach is shown to satisfy a Hopf
algebraic supersymmetry where the difference operator is introduced as a
momentum operator. The breakdown of the Leibniz rule for the lattice difference
operator is accommodated as a coproduct operation of (quasi)triangular Hopf
algebra and the associated field theory is consistently defined as a braided
quantum field theory. Algebraic formulation of path integral is perturbatively
defined and Ward-Takahashi identity can be derived on the lattice. The claimed
inconsistency of the link approach leading to the ordering ambiguity for a
product of fields is solved by introducing an almost trivial braiding structure
corresponding to the triangular structure of the Hopf algebraic superalgebra.
This could be seen as a generalization of spin and statistics relation on the
lattice. From the consistency of this braiding structure of fields a grading
nature for the momentum operator is required.Comment: 45 page
A new large N phase transition in YM2
Inspired by the interpretation of two dimensional Yang-Mills theory on a
cylinder as a random walk on the gauge group, we point out the existence of a
large N transition which is the gauge theory analogue of the cutoff transition
in random walks. The transition occurs in the strong coupling region, with the
't Hooft coupling scaling as alpha*log(N), at a critical value of alpha (alpha
= 4 on the sphere). The two phases below and above the transition are studied
in detail. The effective number of degrees of freedom and the free energy are
found to be proportional to N^(2-alpha/2) below the transition and to vanish
altogether above it. The expectation value of a Wilson loop is calculated to
the leading order and found to coincide in both phases with the strong coupling
value.Comment: 23 pages, 3 figure
Cross-correlation of long-range correlated series
A method for estimating the cross-correlation of long-range
correlated series and , at varying lags and scales , is
proposed. For fractional Brownian motions with Hurst exponents and ,
the asymptotic expression of depends only on the lag
(wide-sense stationarity) and scales as a power of with exponent
for . The method is illustrated on (i) financial series,
to show the leverage effect; (ii) genomic sequences, to estimate the
correlations between structural parameters along the chromosomes.Comment: 14 pages, 8 figure
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
Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2
We propose a new lattice superfield formalism in momentum representation
which accommodates species doublers of the lattice fermions and their bosonic
counterparts as super multiplets. We explicitly show that one dimensional N=2
model with interactions has exact Lie algebraic supersymmetry on the lattice
for all super charges. In coordinate representation the finite difference
operator is made to satisfy Leibnitz rule by introducing a non local product,
the ``star'' product, and the exact lattice supersymmetry is realized. The
standard momentum conservation is replaced on the lattice by the conservation
of the sine of the momentum, which plays a crucial role in the formulation.
Half lattice spacing structure is essential for the one dimensional model and
the lattice supersymmetry transformation can be identified as a half lattice
spacing translation combined with alternating sign structure. Invariance under
finite translations and locality in the continuum limit are explicitly
investigated and shown to be recovered. Supersymmetric Ward identities are
shown to be satisfied at one loop level. Lie algebraic lattice supersymmetry
algebra of this model suggests a close connection with Hopf algebraic exactness
of the link approach formulation of lattice supersymmetry.Comment: 34 pages, 2 figure
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