A solution to the fermion doubling problem for supersymmetric theories on the transverse lattice

Species doubling is a problem that infects most numerical methods that use a spatial lattice. An understanding of species doubling can be found in the Nielsen-Ninomiya theorem which gives a set of conditions that require species doubling. The transverse lattice approach to solving field theories, which has at least one spatial lattice, fails one of the conditions of the Nielsen-Ninomiya theorem nevertheless one still finds species doubling for the standard Lagrangian formulation of the transverse lattice. We will show that the Supersymmetric Discrete Light Cone Quantization (SDLCQ) formulation of the transverse lattice does not have species doubling.Comment: 4 pages, v2: a reference and comments added, the version to appear in Phys. Rev.

Exact Ward-Takahashi identity for the lattice N=1 Wess-Zumino model

The lattice Wess-Zumino model written in terms of the Ginsparg-Wilson relation is invariant under a generalized supersymmetry transformation which is determined by an iterative procedure in the coupling constant. By studying the associated Ward-Takahashi identity up to order $g^2$ we show that this lattice supersymmetry automatically leads to restoration of continuum supersymmetry without fine tuning. In particular, the scalar and fermion renormalization wave functions coincide.Comment: 6 pages, 5 figures, Talk given at QG05, Cala Gonone, Sardinia, Italy. 12-16 September 200

The conceptus induces a switch in protein expression and activities of superoxide dismutase 1 and 2 in the sheep endometrium during early pregnancy

Acknowledgements We thank Philippe Bolifraud (INRA, France), Krawiec Angele, Sandra Grange, Laurence Puillet-Anselme (CHU Grenoble, France) and Margaret Fraser (Aberdeen, UK) for their expert technical assistance. The authors also thank the staff of the sheep sheds of Jouy-en-Josas (INRA, France). The authors would also like to thank the anonymous reviewers for their close examination of this article and their useful comments. Funding This research did not receive any specific grant from any funding agency in the public, commercial or not-for-profit sector.Peer reviewedPostprin

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 ${\cal N}=2, 4$ 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. ${\cal N}=4, 8$ models in three dimensions need fine-tuning of three and one parameters respectively to obtain the desired continuum theories, while two-dimensional models with ${\cal N}=4, 8$ 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

Compact Gauge Fields for Supersymmetric Lattices

We show that a large class of Euclidean extended supersymmetric lattice gauge theories constructed in [hep-lat/0302017 - hep-lat/0503039] can be regarded as compact formulations by using the polar decomposition of the complex link fields. In particular, the gauge part of the supersymmetric lattice action is the standard Wilson action. This formulation facilitates the construction of gauge invariant operators.Comment: 15 pages, 2 figures. Minor change

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

Crossover of the weighted mean fragment mass scaling in 2D brittle fragmentation

We performed vertical and horizontal sandwich 2D brittle fragmentation experiments. The weighted mean fragment mass was scaled using the multiplicity $\mu$. The scaling exponent crossed over at $\log \mu_c \simeq -1.4$. In the small $\mu (\ll\mu_c)$ regime, the binomial multiplicative (BM) model was suitable and the fragment mass distribution obeyed log-normal form. However, in the large $\mu (\gg\mu_c)$ regime, in which a clear power-law cumulative fragment mass distribution was observed, it was impossible to describe the scaling exponent using the BM model. We also found that the scaling exponent of the cumulative fragment mass distribution depended on the manner of impact (loading conditions): it was 0.5 in the vertical sandwich experiment, and approximately 1.0 in the horizontal sandwich experiment.Comment: 5 pages, 3 figure

First results from simulations of supersymmetric lattices

We conduct the first numerical simulations of lattice theories with exact supersymmetry arising from the orbifold constructions of \cite{Cohen:2003xe,Cohen:2003qw,Kaplan:2005ta}. We consider the \cQ=4 theory in $D=0,2$ dimensions and the \cQ=16 theory in $D=0,2,4$ dimensions. We show that the U(N) theories do not possess vacua which are stable non-perturbatively, but that this problem can be circumvented after truncation to SU(N). We measure the distribution of scalar field eigenvalues, the spectrum of the fermion operator and the phase of the Pfaffian arising after integration over the fermions. We monitor supersymmetry breaking effects by measuring a simple Ward identity. Our results indicate that simulations of ${\cal N}=4$ super Yang-Mills may be achievable in the near future.Comment: 25 pages, 14 figures, 9 tables. 3 references adde

Convergence of the Gaussian Expansion Method in Dimensionally Reduced Yang-Mills Integrals

We advocate a method to improve systematically the self-consistent harmonic approximation (or the Gaussian approximation), which has been employed extensively in condensed matter physics and statistical mechanics. We demonstrate the {\em convergence} of the method in a model obtained from dimensional reduction of SU($N$) Yang-Mills theory in $D$ dimensions. Explicit calculations have been carried out up to the 7th order in the large-N limit, and we do observe a clear convergence to Monte Carlo results. For $D \gtrsim 10$ the convergence is already achieved at the 3rd order, which suggests that the method is particularly useful for studying the IIB matrix model, a conjectured nonperturbative definition of type IIB superstring theory.Comment: LaTeX, 4 pages, 5 figures; title slightly changed, explanations added (16 pages, 14 figures), final version published in JHE

T-Duality Transformation and Universal Structure of Non-Critical String Field Theory

We discuss a T-duality transformation for the c=1/2 matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling limit of the Schwinger-Dyson equations and the stochastic Hamiltonian in terms of the dual variables and then compare the results with those using the original spin variables. It is shown that the c=1/2 model in the scaling limit is T-duality symmetric in the sphere approximation. The duality symmetry is however violated when the higher-genus effects are taken into account, owing to the existence of global Z_2 vector fields corresponding to nontrivial homology cycles. Some universal properties of the stochastic Hamiltonians which play an important role in discussing the scaling limit and have been discussed in a previous work by the last two authors are refined in both the original and dual formulations. We also report a number of new explicit results for various amplitudes containing macroscopic loop operators.Comment: RevTex, 46 pages, 5 eps figure