1,708 research outputs found
Exploring the Dynamics of Three-Dimensional Lattice Gauge Theories by External Fields
We investigate the dynamics of three-dimensional lattice gauge theories by
means of an external Abelian magnetic field. For the SU(2) lattice gauge theory
we find evidence of the unstable modes.Comment: 3 pages, PostScript. Contribution to the LATTICE 93 Conference
(Dallas, U.S.A., September 1993) preprint BARI-TH-162/9
Heterotic T-Duality and the Renormalization Group
We consider target space duality transformations for heterotic sigma models
and strings away from renormalization group fixed points. By imposing certain
consistency requirements between the T-duality symmetry and renormalization
group flows, the one loop gauge beta function is uniquely determined, without
any diagram calculations. Classical T-duality symmetry is a valid quantum
symmetry of the heterotic sigma model, severely constraining its
renormalization flows at this one loop order. The issue of heterotic anomalies
and their cancelation is addressed from this duality constraining viewpoint.Comment: 17 pages, Late
Finite-Size Scaling of Vector and Axial Current Correlators
Using quenched chiral perturbation theory, we compute the long-distance
behaviour of two-point functions of flavour non-singlet axial and vector
currents in a finite volume, for small quark masses, and at a fixed gauge-field
topology. We also present the corresponding predictions for the unquenched
theory at fixed topology. These results can in principle be used to measure the
low-energy constants of the chiral Lagrangian, from lattice simulations in
volumes much smaller than one pion Compton wavelength. We show that quenching
has a dramatic effect on the vector correlator, which is argued to vanish to
all orders, while the axial correlator appears to be a robust observable only
moderately sensitive to quenching.Comment: version to appear in NP
Analytic Representations of Yang-Mills Amplitudes
Scattering amplitudes in Yang-Mills theory can be represented in the
formalism of Cachazo, He and Yuan (CHY) as integrals over an auxiliary
projective space---fully localized on the support of the scattering equations.
Because solving the scattering equations is difficult and summing over the
solutions algebraically complex, a method of directly integrating the terms
that appear in this representation has long been sought. We solve this
important open problem by first rewriting the terms in a manifestly
Mobius-invariant form and then using monodromy relations (inspired by analogy
to string theory) to decompose terms into those for which combinatorial rules
of integration are known. The result is a systematic procedure to obtain
analytic, covariant forms of Yang-Mills tree-amplitudes for any number of
external legs and in any number of dimensions. As examples, we provide compact
analytic expressions for amplitudes involving up to six gluons of arbitrary
helicities.Comment: 29 pages, 43 figures; also included is a Mathematica notebook with
explicit formulae. v2: citations added, and several (important) typos fixe
Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
We prove that the scattering equation formalism for Yang-Mills amplitudes can
be used to make manifest the theory's color-kinematics duality. This is
achieved through a concrete reduction algorithm which renders this duality
manifest term-by-term. The reduction follows from the recently derived set of
identities for amplitudes expressed in the scattering equation formalism that
are analogous to monodromy relations in string theory. A byproduct of our
algorithm is a generalization of the identities among gravity and Yang-Mills
amplitudes.Comment: 20 pages, 20 figure
Scattering Equations and Feynman Diagrams
We show a direct matching between individual Feynman diagrams and integration
measures in the scattering equation formalism of Cachazo, He and Yuan. The
connection is most easily explained in terms of triangular graphs associated
with planar Feynman diagrams in -theory. We also discuss the
generalization to general scalar field theories with interactions,
corresponding to polygonal graphs involving vertices of order . Finally, we
describe how the same graph-theoretic language can be used to provide the
precise link between individual Feynman diagrams and string theory integrands.Comment: 18 pages, 57 figure
Spectral Properties of the Overlap Dirac Operator in QCD
We discuss the eigenvalue distribution of the overlap Dirac operator in
quenched QCD on lattices of size 8^{4}, 10^{4} and 12^{4} at \beta = 5.85 and
\beta = 6. We distinguish the topological sectors and study the distributions
of the leading non-zero eigenvalues, which are stereographically mapped onto
the imaginary axis. Thus they can be compared to the predictions of random
matrix theory applied to the \epsilon-expansion of chiral perturbation theory.
We find a satisfactory agreement, if the physical volume exceeds about (1.2
fm)^{4}. For the unfolded level spacing distribution we find an accurate
agreement with the random matrix conjecture on all volumes that we considered.Comment: 16 pages, 8 figures, final version published in JHE
Integration Rules for Scattering Equations
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum
field theories can be represented as integrals that are fully localized on
solutions to the so-called scattering equations. Because the number of
solutions to the scattering equations grows quite rapidly, the contour of
integration involves contributions from many isolated components. In this
paper, we provide a simple, combinatorial rule that immediately provides the
result of integration against the scattering equation constraints for any
M\"obius-invariant integrand involving only simple poles. These rules have a
simple diagrammatic interpretation that makes the evaluation of any such
integrand immediate. Finally, we explain how these rules are related to the
computation of amplitudes in the field theory limit of string theory.Comment: 30 pages, 29 figure
Integration Rules for Loop Scattering Equations
We formulate new integration rules for one-loop scattering equations
analogous to those at tree-level, and test them in a number of non-trivial
cases for amplitudes in scalar -theory. This formalism greatly
facilitates the evaluation of amplitudes in the CHY representation at one-loop
order, without the need to explicitly sum over the solutions to the loop-level
scattering equations.Comment: 22 pages, 17 figure
Fine‐scale measurement of diffusivity in a microbial mat with nuclear magnetic resonance imaging
Noninvasive 1H‐nuclear magnetic resonance (NMR) imaging was used to investigate the diffusive properties of microbial mats in two dimensions. Pulsed field gradient NMR was used to acquire images of the H2O diffusion coefficient, Ds, and multiecho imaging NMR was used to obtain images of the water density in two structurally different microbial mats sampled from Solar Lake (Egypt). We found a pronounced lateral and vertical variability of both water density and water diffusion coefficient, correlated with the laminated and heterogeneous distribution of microbial cells and exopolymers within the mats. The average water density varied from 0.5 to 0.9, whereas the average water diffusion coefficient ranged from 0.4 to 0.9 relative to the values obtained in the stagnant water above the mat samples. The apparent water diffusivities estimated from NMR imaging compared well to apparent O2 diffusivities measured with a diffusivity microsensor. Analysis of measured O2 concentration profiles with a diffusion‐reaction model showed that both the magnitude of calculated rates and the depth distribution of calculated O2 consumption/production zones changed when the observed variations of diffusivity were taken into account. With NMR imaging, diffusivity can be determined at high spatial resolution, which can resolve inherent lateral and vertical heterogeneities found in most natural benthic systems
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