352 research outputs found
The Global Renormalization Group Trajectory in a Critical Supersymmetric Field Theory on the Lattice Z^3
We consider an Euclidean supersymmetric field theory in given by a
supersymmetric perturbation of an underlying massless Gaussian measure
on scalar bosonic and Grassmann fields with covariance the Green's function of
a (stable) L\'evy random walk in . The Green's function depends on the
L\'evy-Khintchine parameter with . For
the interaction is marginal. We prove for
sufficiently small and initial
parameters held in an appropriate domain the existence of a global
renormalization group trajectory uniformly bounded on all renormalization group
scales and therefore on lattices which become arbitrarily fine. At the same
time we establish the existence of the critical (stable) manifold. The
interactions are uniformly bounded away from zero on all scales and therefore
we are constructing a non-Gaussian supersymmetric field theory on all scales.
The interest of this theory comes from the easily established fact that the
Green's function of a (weakly) self-avoiding L\'evy walk in is a second
moment (two point correlation function) of the supersymmetric measure governing
this model. The control of the renormalization group trajectory is a
preparation for the study of the asymptotics of this Green's function. The
rigorous control of the critical renormalization group trajectory is a
preparation for the study of the critical exponents of the (weakly)
self-avoiding L\'evy walk in .Comment: 82 pages, Tex with macros supplied. Revision includes 1. redefinition
of norms involving fermions to ensure uniqueness. 2. change in the definition
of lattice blocks and lattice polymer activities. 3. Some proofs have been
reworked. 4. New lemmas 5.4A, 5.14A, and new Theorem 6.6. 5.Typos
corrected.This is the version to appear in Journal of Statistical Physic
A simple method for finite range decomposition of quadratic forms and Gaussian fields
We present a simple method to decompose the Green forms corresponding to a
large class of interesting symmetric Dirichlet forms into integrals over
symmetric positive semi-definite and finite range (properly supported) forms
that are smoother than the original Green form. This result gives rise to
multiscale decompositions of the associated Gaussian free fields into sums of
independent smoother Gaussian fields with spatially localized correlations. Our
method makes use of the finite propagation speed of the wave equation and
Chebyshev polynomials. It improves several existing results and also gives
simpler proofs.Comment: minor correction for t<
Kosterlitz-Thouless Transition Line for the Two Dimensional Coulomb Gas
With a rigorous renormalization group approach, we study the pressure of the
two dimensional Coulomb Gas along a small piece of the Kosterlitz-Thouless
transition line, i.e. the boundary of the dipole region in the
activity-temperature phase-space.Comment: 61 pages, 2 figure
Quark Confinement and Dual Representation in 2+1 Dimensional Pure Yang-Mills Theory
We study the quark confinement problem in 2+1 dimensional pure Yang-Mills
theory using euclidean instanton methods. The instantons are regularized and
dressed Wu-Yang monopoles. The dressing of a monopole is due to the mean field
of the rest of the monopoles. We argue that such configurations are stable to
small perturbations unlike the case of singular, undressed monopoles. Using
exact non-perturbative results for the 3-dim. Coulomb gas, where Debye
screening holds for arbitrarily low temperatures, we show in a self-consistent
way that a mass gap is dynamically generated in the gauge theory. The mass gap
also determines the size of the monopoles. In a sense the pure Yang-Mills
theory generates a dynamical Higgs effect. We also identify the disorder
operator of the model in terms of the Sine-Gordon field of the Coulomb gas.Comment: 26 pages, RevTex, Title changed, a new section added, the discussion
on stability of dressed monopole expanded. Version to appear in Physical
Review
Garment worker rights and the fashion industry’s response to COVID-19
© The Author(s) 2020. In this commentary, we examine the fashion industry’s early responses to COVID-19. Looking across fashion’s global production networks, we argue the fashion industry’s response has been rapid, yet highly inequitable, reflecting—and further entrenching—existing inequalities in the industry
Will COVID-19 support the transition to a more sustainable fashion industry?
In this policy brief, we examine the impact of COVID-19 on sustainability initiatives in the fashion industry. We ask whether COVID-19 is likely to support the transition to a more sustainable fashion industry. In answering this question, we utilize a framework for examining sustainability along the fashion-supply chain, highlighting the opportunities and challenges for a sustainable transition with respect to design, production, retail, consumption, and end-of-life. At each step, we also consider socioeconomic dimensions with regard to social impacts, employment, and gender. In doing so, we argue that any meaningful shift toward sustainability and a just transition must recognize social and environmental challenges as interconnected, addressing structural inequalities
Vortices and confinement at weak coupling
We discuss the physical picture of thick vortices as the mechanism
responsible for confinement at arbitrarily weak coupling in SU(2) gauge theory.
By introducing appropriate variables on the lattice we distinguish between
thin, thick and `hybrid' vortices, the latter involving Z(2) monopole loop
boundaries. We present numerical lattice simulation results that demonstrate
that the full SU(2) string tension at weak coupling arises from the presence of
vortices linked to the Wilson loop. Conversely, excluding linked vortices
eliminates the confining potential. The numerical results are stable under
alternate choice of lattice action as well as a smoothing procedure which
removes short distance fluctuations while preserving long distance physics.Comment: 21 pages, LaTe
On the spatial Markov property of soups of unoriented and oriented loops
We describe simple properties of some soups of unoriented Markov loops and of
some soups of oriented Markov loops that can be interpreted as a spatial Markov
property of these loop-soups. This property of the latter soup is related to
well-known features of the uniform spanning trees (such as Wilson's algorithm)
while the Markov property of the former soup is related to the Gaussian Free
Field and to identities used in the foundational papers of Symanzik, Nelson,
and of Brydges, Fr\"ohlich and Spencer or Dynkin, or more recently by Le Jan
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