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

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

Learning In the Visual Arts and the Worldviews of Young Children

This paper reports a research study into the effects of rich,sustained visual arts instruction on 103inner city 9-year-olds in two major US cities. We use the lenses of social learning theory, theories of motivation and self-efficacy, and recentresearch on artistic thinking to investigate the programs' effects on children's self-beliefs and creative thinking. The study enlisted a pre -- post measure,treatment-comparison group design along with structured observations of participant andcomparison group classrooms. The arts students made significant comparative gains on a selfefficacy scale and on an 'originality' subscale of a standard creativity test. These effects are attributed to children's engagement in art and to the social organization of instruction includingreinforcing peer and student -- adult relationships. Relationships between self-efficacy beliefs andtendencies to think originally are explored

A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice

We propose a discretization of two dimensional Euclidean Yang-Mills theories with N=2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum super Yang Mills action which we show may be written in terms of two real Kahler-Dirac fields whose components transform into each other under the twisted supersymmetry. Once the theory is written in this geometrical language it is straightforward to discretize by mapping the component tensor fields to appropriate geometrical structures in the lattice and by replacing the continuum exterior derivative and its adjoint by appropriate lattice covariant difference operators. The lattice action is local and possesses a unique vacuum state while the use of Kahler-Dirac fermions ensures the model does not exhibit spectrum doubling.Comment: Minor typos fixed. Version to be published in JHE

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

Towards lattice simulation of the gauge theory duals to black holes and hot strings

A generalization of the AdS/CFT conjecture postulates a duality between IIA string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't Hooft limit. At low temperatures string theory describes black holes, whose thermodynamics may hence be studied using the dual quantum mechanics. This quantum mechanics is strongly coupled which motivates the use of lattice techniques. We argue that, contrary to expectation, the theory when discretized naively will nevertheless recover continuum supersymmetry as the lattice spacing is sent to zero. We test these ideas by studying the 4 supercharge version of this Yang-Mills quantum mechanics in the 't Hooft limit. We use both a naive lattice action and a manifestly supersymmetric action. Using Monte Carlo methods we simulate the Euclidean theories, and study the lattice continuum limit, for both thermal and non-thermal periodic boundary conditions, confirming continuum supersymmetry is recovered for the naive action when appropriate. We obtain results for the thermal system with N up to 12. These favor the existence of a single deconfined phase for all non-zero temperatures. These results are an encouraging indication that the 16 supercharge theory is within reach using similar methods and resources.Comment: 49 pages, 14 figure

Random manifolds and quantum gravity

The non-perturbative, lattice field theory approach towards the quantization of Euclidean gravity is reviewed. Included is a tentative summary of the most significant results and a presentation of the current state of art.Comment: invited plenary talk at LATTICE '99 (Pisa), latex 5p

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

Shape transformations of a model of self-avoiding triangulated surfaces of sphere topology

We study a surface model with a self-avoiding (SA) interaction using the canonical Monte Carlo simulation technique on fixed-connectivity (FC) triangulated lattices of sphere topology. The model is defined by an area energy, a deficit angle energy, and the SA potential. A pressure term is also included in the Hamiltonian. The volume enclosed by the surface is well defined because of the self-avoidance. We focus on whether or not the interaction influences the phase structure of the FC model under two different conditions of pressure ${\it \Delta} p$; zero and small negative. The results are compared with the previous results of the self-intersecting model, which has a rich variety of phases; the smooth spherical phase, the tubular phase, the linear phase, and the collapsed phase. We find that the influence of the SA interaction on the multitude of phases is almost negligible except for the evidence that no crumpled surface appears under {\it \Delta} p\=\0 at least even in the limit of zero bending rigidity \alpha\to \0. The Hausdorff dimension is obtained in the limit of \alpha\to \0 and compared with previous results of SA models, which are different from the one in this paper.Comment: 9 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