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

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

Bayesian Analysis of Many-Pole Fits of Hadron Propagators in Lattice QCD

We use Bayes' probability theorem to analyze many-pole fits of hadron propagators. An alternative method of estimating values and uncertainties of the fit parameters is offered, which has certain advantages over the conventional methods. The probability distribution of the parameters of a fit is calculated. The relative probability of various models is calculated.Comment: 4 pages, 6 figures, Latex with espcrc2.sty, uuencoded compressed tar file contains 7 Latex files: 1 with the paper and 6 with the figures. Talk presented at LATTICE96(spectrum

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

Steiner Variations on Random Surfaces

Ambartzumian et.al. suggested that the modified Steiner action functional had desirable properties for a random surface action. However, Durhuus and Jonsson pointed out that such an action led to an ill-defined grand-canonical partition function and suggested that the addition of an area term might improve matters. In this paper we investigate this and other related actions numerically for dynamically triangulated random surfaces and compare the results with the gaussian plus extrinsic curvature actions that have been used previously.Comment: 8 page

Thermal phases of D1-branes on a circle from lattice super Yang-Mills

We report on the results of numerical simulations of 1+1 dimensional SU(N) Yang-Mills theory with maximal supersymmetry at finite temperature and compactified on a circle. For large N this system is thought to provide a dual description of the decoupling limit of N coincident D1-branes on a circle. It has been proposed that at large N there is a phase transition at strong coupling related to the Gregory-Laflamme (GL) phase transition in the holographic gravity dual. In a high temperature limit there was argued to be a deconfinement transition associated to the spatial Polyakov loop, and it has been proposed that this is the continuation of the strong coupling GL transition. Investigating the theory on the lattice for SU(3) and SU(4) and studying the time and space Polyakov loops we find evidence supporting this. In particular at strong coupling we see the transition has the parametric dependence on coupling predicted by gravity. We estimate the GL phase transition temperature from the lattice data which, interestingly, is not yet known directly in the gravity dual. Fine tuning in the lattice theory is avoided by the use of a lattice action with exact supersymmetry.Comment: 21 pages, 8 figures. v2: References added, two figures were modified for clarity. v3: Normalisation of lattice coupling corrected by factor of two resulting in change of estimate for c_cri

Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group

We propose a lattice model for two-dimensional SU(N) N=(2,2) super Yang-Mills model. We start from the CKKU model for this system, which is valid only for U(N) gauge group. We give a reduction of U(1) part keeping a part of supersymmetry. In order to suppress artifact vacua, we use an admissibility condition.Comment: 16 pages, 3 figures; v2: typo crrected; v3: 18 pages, a version to appear in JHE

Supersymmetric Yang--Mills theories with exact supersymmetry on the lattice

Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang--Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean spacetime lattice. Such theories are known as maximally twisted SYM theories. In this review we discuss the construction and some applications of such classes of theories. The one-loop perturbative renormalization of the four-dimensional lattice ${\cal N}=4$ SYM is discussed in particular. The lattice theories constructed using twisted approach play an important role in investigating the thermal phases of strongly coupled SYM theories and also the thermodynamic properties of their dual gravitational theories.Comment: 74 pages, 15 figures, minor revision, references added, published versio

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

An anisotropic hybrid non-perturbative formulation for 4D N = 2 supersymmetric Yang-Mills theories

We provide a simple non-perturbative formulation for non-commutative four-dimensional N = 2 supersymmetric Yang-Mills theories. The formulation is constructed by a combination of deconstruction (orbifold projection), momentum cut-off and matrix model techniques. We also propose a moduli fixing term that preserves lattice supersymmetry on the deconstruction formulation. Although the analogous formulation for four-dimensional N = 2 supersymmetric Yang-Mills theories is proposed also in Nucl.Phys.B857(2012), our action is simpler and better suited for computer simulations. Moreover, not only for the non-commutative theories, our formulation has a potential to be a non-perturbative tool also for the commutative four-dimensional N = 2 supersymmetric Yang-Mills theories.Comment: 32 pages, final version accepted in JHE