We discuss the implementation of the "direct" maximal center gauge (a gauge which maximizes the lattice average of the squared-modulus of the trace of link variables), and its use in identifying Z 2 center vortices in Yang-Mills vacuum configurations generated by lattice Monte Carlo. We find that center vortices identified in the vacuum state account for the full asymptotic string tension. Scaling of vortex densities with lattice coupling, change in vortex size with cooling, and sensitivity to Gribov copies is discussed. Preliminary evidence is presented, on small lattices, for center dominance in SU(3) lattice gauge theory.

We report on numerical simulations of SU (2) lattice gauge theory with two flavors of light dynamical quarks in the adjoint of the gauge group. The dynamics of this theory is thought to be very different from QCD -the theory exhibiting conformal or near conformal behavior in the infrared. We make a high resolution survey of the phase diagram of this model in the plane of the bare coupling and quark mass on lattices of size 8 3 × 16. Our simulations reveal a line of first order phase transitions extending from β = 0 to β = β c ∼ 2.0. For β > β c the phase boundary is no longer first order but continues as the locus of minimum meson mass. For β > β c we observe the pion and rho masses along the phase boundary to be light, independent of bare coupling and approximately degenerate. We discuss possible interpretations of these observations and corresponding continuum limits.

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Maximally supersymmetric Yang-Mills theory in four dimensions can be formulated on a spacetime lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice theory, paying particular attention to its strongly coupled regime. Targeting a theory with gauge group SU(N ), the lattice formulation is naturally described in terms of gauge group U(N ). Although the U(1) degrees of freedom decouple in the continuum limit we show that these degrees of freedom lead to unwanted lattice artifacts at strong coupling. We demonstrate that these lattice artifacts can be removed, leaving behind a lattice formulation based on the SU(N ) gauge group with the expected apparently conformal behavior at both weak and strong coupling.

We find that Polyakov lines, computed in abelian-projected SU(2) lattice gauge theory in the confined phase, have finite expectation values for lines corresponding to two units of the abelian electric charge. This means that the abelian-projected lattice has at most Z 2 , rather than U(1), global symmetry. We also find a severe breakdown of the monopole dominance approximation, as well as positivity, in this charge-2 case. These results imply that the abelian-projected lattice is not adequately represented by a monopole Coulomb gas; the data is, however, consistent with a center vortex structure. Further evidence is provided, in lattice Monte Carlo simulations, for collimation of confining color-magnetic flux into vortices.

The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge theories described in hep-lat/0605003 uses exact lattice chirality to decouple the massless chiral fermions from a mirror sector, whose strong dynamics is conjectured to give cutoff-scale mass to the mirror fermions without breaking the chiral gauge symmetry. In this paper, we study the mirror sector dynamics of a two-dimensional chiral gauge theory in the limit of strong Yukawa and vanishing gauge couplings, in which case it reduces to an XY model coupled to Ginsparg-Wilson fermions. For the mirror fermions to acquire cutoff-scale mass it is believed to be important that the XY model remain in its "high temperature" phase, where there is no algebraic ordering-a conjecture supported by the results of our work. We use analytic and Monte-Carlo methods with dynamical fermions to study the scalar and fermion susceptibilities, and the mirror fermion spectrum. Our results provide convincing evidence that the strong dynamics does not "break" the chiral symmetry (more precisely, that the mirror fermions do not induce algebraic ordering in two-dimensions), and that the mirror fermions decouple from the infrared physics.

Inequivalent standard-like observable sector embeddings in Z 3 orbifolds with two discrete Wilson lines, as determined by Casas, Mondragon, and Muñoz, are completed by examining all possible ways of embedding the hidden sector. The hidden sector embeddings are relevant to twisted matter in nontrivial representations of the Standard Model and to scenarios where supersymmetry breaking is generated in a hidden sector. We find a set of 175 models which have a hidden sector gauge group which is viable for dynamical supersymmetry breaking. Only four different hidden sector gauge groups are possible in these models. C 2001 Academic PressOne of the distasteful aspects of four-dimensional heterotic string phenomenology is the glut of vacua possible in even the most elementary compactification schemes. For instance, the lowly Z 3 orbifold [1] admits an enormously large number of low energy effective theories, once nonstandard embeddings-including discrete Wilson lines (described below)-are allowed. (The embedding dictates how the space group-the transformation group used to construct the orbifold-affects the gauge degrees of freedom in the underlying string theory. For a recent review of heterotic orbifolds, see [2].) However, it was pointed out some time ago by Casas, Mondragon, and Muñoz (CMM) that most of the embeddings are actually redundant, and only a relatively small set of inequivalent embeddings exist [3].In heterotic Z 3 orbifold models with discrete Wilson lines, the embedding is expressed in terms of four sixteen-dimensional vectors: the twist embedding V and three Wilson lines a 1 , a 3 , and a 5 ; each of the four vectors is given by one-third of a vector belonging to the E 8 × E 8 root lattice (denoted here as E 8 ×E 8 ):(In Appendix A we provide a brief review of the E 8 and E 8 × E 8 root systems, including explicit realizations of the respective root lattices E 8 and E 8 ×E 8 .) It is convenient to denote the vector formed from the first eight entries of V by V A and the vector formed from the last eight entries of V by V B , so that the twist embedding V may be written as V = (V A ; V B ). Equation (1) then implies

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.