Finite-size-scaling functions for 3d O(4) and O(2) spin models and QCD

We calculate numerically universal finite-size-scaling functions for the three-dimensional O(4) and O(2) models. The approach of these functions to the infinite-volume scaling functions is studied in detail on the critical and pseudocritical lines. For this purpose we determine the pseudocritical line in two different ways. We find that the asymptotic form of the finite-size-scaling functions is already reached at small values of the scaling variable. A comparison with QCD lattice data for two flavours of staggered fermions shows a similar finite-size behaviour which is compatible with that of the spin models.Comment: 14 pages, 14 Ps-figures, Latex2

Equation of state and Goldstone-mode effects of the three-dimensional O(2) model

We investigate numerically the three-dimensional O(2) model on 8^3-160^3 lattices as a function of the magnetic field H. In the low-temperature phase we verify the H-dependence of the magnetization M induced by Goldstone modes and determine M in the thermodynamic limit both by extrapolation and by chiral perturbation theory. This enables us to calculate the corresponding critical amplitude. At T_c the critical scaling behaviour of the magnetization as a function of H is used to determine another critical amplitude. In both cases we find negative corrections-to-scaling. Our low-temperature results are well described by the perturbative form of the model's magnetic equation of state, with coefficients determined nonperturbatively from our data. The O(2) scaling function for the magnetization is found to have a smaller slope than the one for the O(4) model.Comment: 15 pages, Latex2e, Fig.6b replaced, several comments and two references added, final version for Phys. Lett.

The Nucleon Electric Dipole Form Factor From Dimension-Six Time-Reversal Violation

We calculate the electric dipole form factor of the nucleon that arises as a low-energy manifestation of time-reversal violation in quark-gluon interactions of effective dimension 6: the quark electric and chromoelectric dipole moments, and the gluon chromoelectric dipole moment. We use the framework of two-flavor chiral perturbation theory to one loop

Dynamics at a smeared phase transition

We investigate the effects of rare regions on the dynamics of Ising magnets with planar defects, i.e., disorder perfectly correlated in two dimensions. In these systems, the magnetic phase transition is smeared because static long-range order can develop on isolated rare regions. We first study an infinite-range model by numerically solving local dynamic mean-field equations. Then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean-field theory. In the tail region of the smeared transition the dynamics is even slower than in a conventional Griffiths phase: the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times.Comment: 10 pages, 8eps figures included, final version as publishe

J.S. Bell's Concept of Local Causality

John Stewart Bell's famous 1964 theorem is widely regarded as one of the most important developments in the foundations of physics. It has even been described as "the most profound discovery of science." Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many textbooks and commentators report that Bell's theorem refutes the possibility (suggested especially by Einstein, Podolsky, and Rosen in 1935) of supplementing ordinary quantum theory with additional ("hidden") variables that might restore determinism and/or some notion of an observer-independent reality. On this view, Bell's theorem supports the orthodox Copenhagen interpretation. Bell's own view of his theorem, however, was quite different. He instead took the theorem as establishing an "essential conflict" between the now well-tested empirical predictions of quantum theory and relativistic \emph{local causality}. The goal of the present paper is, in general, to make Bell's own views more widely known and, in particular, to explain in detail Bell's little-known mathematical formulation of the concept of relativistic local causality on which his theorem rests. We thus collect and organize many of Bell's crucial statements on these topics, which are scattered throughout his writings, into a self-contained, pedagogical discussion including elaborations of the concepts "beable", "completeness", and "causality" which figure in the formulation. We also show how local causality (as formulated by Bell) can be used to derive an empirically testable Bell-type inequality, and how it can be used to recapitulate the EPR argument.Comment: 19 pages, 4 figure

Hybrid meson decay from the lattice

We discuss the allowed decays of a hybrid meson in the heavy quark limit. We deduce that an important decay will be into a heavy quark non-hybrid state and a light quark meson, in other words, the de-excitation of an excited gluonic string by emission of a light quark-antiquark pair. We discuss the study of hadronic decays from the lattice in the heavy quark limit and apply this approach to explore the transitions from a spin-exotic hybrid to $\chi_b \eta$ and $\chi_b S$ where $S$ is a scalar meson. We obtain a signal for the transition emitting a scalar meson and we discuss the phenomenological implications.Comment: 18 pages, LATEX, 3 ps figure

Adjoint "quarks" on coarse anisotropic lattices: Implications for string breaking in full QCD

A detailed study is made of four dimensional SU(2) gauge theory with static adjoint ``quarks'' in the context of string breaking. A tadpole-improved action is used to do simulations on lattices with coarse spatial spacings $a_s$, allowing the static potential to be probed at large separations at a dramatically reduced computational cost. Highly anisotropic lattices are used, with fine temporal spacings $a_t$, in order to assess the behavior of the time-dependent effective potentials. The lattice spacings are determined from the potentials for quarks in the fundamental representation. Simulations of the Wilson loop in the adjoint representation are done, and the energies of magnetic and electric ``gluelumps'' (adjoint quark-gluon bound states) are calculated, which set the energy scale for string breaking. Correlators of gauge-fixed static quark propagators, without a connecting string of spatial links, are analyzed. Correlation functions of gluelump pairs are also considered; similar correlators have recently been proposed for observing string breaking in full QCD and other models. A thorough discussion of the relevance of Wilson loops over other operators for studies of string breaking is presented, using the simulation results presented here to support a number of new arguments.Comment: 22 pages, 14 figure

Hidden sl(2,R) Symmetry in 2D CFTs and the Wave Function of 3D Quantum Gravity

We show that all two-dimensional conformal field theories possess a hidden sl(2,R) affine symmetry. More precisely, we add appropriate ghost fields to an arbitrary CFT, and we use them to construct the currents of sl(2,R). We then define a BRST operator whose cohomology defines a physical subspace where the extended theory coincides with the original CFT. We use the sl(2,R) algebra to construct candidate wave functions for 3-d quantum gravity coupled to matter, and we discuss their viability.Comment: Minor misprints corrected.Eight references added. To appear in JHEP.34 pages, LaTe

Flux-tubes in three-dimensional lattice gauge theories

Flux-tubes in different representations of SU(2) and U(1) lattice gauge theories in three dimensions are measured. Wilson loops generate heavy ``quark-antiquark'' pairs in fundamental ($j=1/2$), adjoint ($j=1$), and quartet ($j=3/2$) representations of SU(2). The first direct lattice measurements of the flux-tube cross-section ${\cal A}_j$ as a function of representation are made. It is found that ${\cal A}_j \approx {\rm constant}$, to about 10\%. Results are consistent with a connection between the string tension $\sigma_j$ and ${\cal A}_j$ suggested by a simplified flux-tube model, $\sigma_j = g^2 j(j+1) / (2 {\cal A}_j)$ [$g$ is the gauge coupling], given that $\sigma_j$ scales like the Casimir $j(j+1)$, as observed in previous lattice studies in both three and four dimensions. The results can discriminate among phenomenological models of the physics underlying confinement. Flux-tubes for singly- and doubly-charged Wilson loops in compact QED$_3$ are also measured. It is found that the string tension scales as the squared-charge and the flux-tube cross-section is independent of charge to good approximation. These SU(2) and U(1) simulations lend some support, albeit indirectly, to a conjecture that the dual superconductor mechanism underlies confinement in compact gauge theories in both three and four dimensions.Comment: 15 pages (REVTEX 2.1). Figures: 11, not included (available by request from [email protected] by regular mail, postscript files, or one self-unpacking uuencoded file