1,021 research outputs found
Renormalization of composite operators
The blocked composite operators are defined in the one-component Euclidean
scalar field theory, and shown to generate a linear transformation of the
operators, the operator mixing. This transformation allows us to introduce the
parallel transport of the operators along the RG trajectory. The connection on
this one-dimensional manifold governs the scale evolution of the operator
mixing. It is shown that the solution of the eigenvalue problem of the
connection gives the various scaling regimes and the relevant operators there.
The relation to perturbative renormalization is also discussed in the framework
of the theory in dimension .Comment: 24 pages, revtex (accepted by Phys. Rev. D), changes in introduction
and summar
Ising Spin Glasses on Wheatstone-Bridge Hierarchical Lattices
Nearest-neighbor-interaction Ising spin glasses are studied on three
different hierarchical lattices, all of them belonging to the Wheatstone-Bridge
family. It is shown that the spin-glass lower critical dimension in these
lattices should be greater than 2.32. Finite-temperature spin-glass phases are
found for a lattice of fractal dimension (whose unit cell is
obtained from a simple construction of a part of the cubic lattice), as well as
for a lattice of fractal dimension close to five.Comment: Accepted for publication in Physics Letters
Renormalization group flows for gauge theories in axial gauges
Gauge theories in axial gauges are studied using Exact Renormalisation Group flows. We introduce a background field in the infrared regulator, but not in the gauge fixing, in contrast to the usual background field gauge. It is shown how heat-kernel methods can be used to obtain approximate solutions to the flow and the corresponding Ward identities. Expansion schemes are discussed, which are not applicable in covariant gauges. As an application, we derive the one-loop effective action for covariantly constant field strength, and the one-loop beta-function for arbitrary regulator
Monte Carlo and Renormalization Group Effective Potentials in Scalar Field Theories
We study constraint effective potentials for various strongly interacting
theories. Renormalization group (RG) equations for these quantities
are discussed and a heuristic development of a commonly used RG approximation
is presented which stresses the relationships among the loop expansion, the
Schwinger-Dyson method and the renormalization group approach. We extend the
standard RG treatment to account explicitly for finite lattice effects.
Constraint effective potentials are then evaluated using Monte Carlo (MC)
techniques and careful comparisons are made with RG calculations. Explicit
treatment of finite lattice effects is found to be essential in achieving
quantitative agreement with the MC effective potentials. Excellent agreement is
demonstrated for and , O(1) and O(2) cases in both symmetric and
broken phases.Comment: 16 pages, 4 figures appended to end of this fil
Wegner-Houghton equation and derivative expansion
We study the derivative expansion for the effective action in the framework
of the Exact Renormalization Group for a single component scalar theory. By
truncating the expansion to the first two terms, the potential and the
kinetic coefficient , our analysis suggests that a set of coupled
differential equations for these two functions can be established under certain
smoothness conditions for the background field and that sharp and smooth
cut-off give the same result. In addition we find that, differently from the
case of the potential, a further expansion is needed to obtain the differential
equation for , according to the relative weight between the kinetic and
the potential terms. As a result, two different approximations to the
equation are obtained. Finally a numerical analysis of the coupled equations
for and is performed at the non-gaussian fixed point in
dimensions to determine the anomalous dimension of the field.Comment: 15 pages, 3 figure
Holographic renormalisation group flows and renormalisation from a Wilsonian perspective
From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular fixed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satisfied by the Wilson action and find the corresponding fixed points and their eigendeformations, which have a diagonal evolution close to the fixed points. The relevant eigendeformations are used to construct renormalised theories. We explore the relation of this formalism with holographic renormalisation. We also discuss different renormalisation schemes and show that the solutions to the gravity equations of motion can be used as renormalised couplings that parametrise the renormalised theories. This provides a transparent connection between holographic renormalisation group flows in the Wilsonian and non-Wilsonian approaches. The general results are illustrated by explicit calculations in an interacting scalar theory in AdS space
Prospective evaluation of quality of life after conventional abdominal aortic aneurysm surgery
Objectives:To evaluate the changes in quality of life following conventional abdominal aortic aneurysm repair.Design:Prospective study.Materials and methods:Fifty-nine consecutive patients (50 men; nine women) in two surgical centres were investigated preoperatively, and at 6 weeks, 3 months and 6 months postoperatively. Quality of life was measured using the Short Form 36 (SF 36) questionnaire and the York Quality of Life questionnaire, from which the Rosser index was calculated.Results:Rosser index assessment showed restoration of quality of life to preoperative levels by 3 months, and significant improvement at 6 months. Changes in the SF 36 revealed significant improvement in mental health, and physical role limitation at all times postoperatively. Social function worsened at 6 weeks but improved to preoperative levels by 3 and 6 months after surgery.Conclusions:Quality of life was improved after open aortic aneurysm repair. The time course of recovery shows a predominant improvement between 6 weeks and 3 months postoperatively
N=1* model and glueball superpotential from Renormalization-Group-improved perturbation theory
A method for computing the low-energy non-perturbative properties of SUSY
GFT, starting from the microscopic lagrangian model, is presented. The method
relies on covariant SUSY Feynman graph techniques, adapted to low energy, and
Renormalization-Group-improved perturbation theory. We apply the method to
calculate the glueball superpotential in N=1 SU(2) SYM and obtain a potential
of the Veneziano-Yankielowicz type.Comment: 19 pages, no figures; added references; note added at the end of the
paper; version to appear in JHE
Tachyon Condensation, Open-Closed Duality, Resolvents, and Minimal Bosonic and Type 0 Strings
Type 0A string theory in the (2,4k) superconformal minimal model backgrounds
and the bosonic string in the (2,2k-1) conformal minimal models, while
perturbatively identical in some regimes, may be distinguished
non-perturbatively using double scaled matrix models. The resolvent of an
associated Schrodinger operator plays three very important interconnected
roles, which we explore perturbatively and non-perturbatively. On one hand, it
acts as a source for placing D-branes and fluxes into the background, while on
the other, it acts as a probe of the background, its first integral yielding
the effective force on a scaled eigenvalue. We study this probe at disc, torus
and annulus order in perturbation theory, in order to characterize the effects
of D-branes and fluxes on the matrix eigenvalues. On a third hand, the
integrated resolvent forms a representation of a twisted boson in an associated
conformal field theory. The entire content of the closed string theory can be
expressed in terms of Virasoro constraints on the partition function, which is
realized as wavefunction in a coherent state of the boson. Remarkably, the
D-brane or flux background is simply prepared by acting with a vertex operator
of the twisted boson. This generates a number of sharp examples of open-closed
duality, both old and new. We discuss whether the twisted boson conformal field
theory can usefully be thought of as another holographic dual of the
non-critical string theory.Comment: 37 pages, some figures, LaTe
Stochastic Quantization vs. KdV Flows in 2D Quantum Gravity
We consider the stochastic quantization scheme for a non-perturbative
stabilization of 2D quantum gravity and prove that it does not satisfy the KdV
flow equations. It therefore differs from a recently suggested matrix model
which allows real solutions to the KdV equations. The behaviour of the Fermi
energy, the free energy and macroscopic loops in the stochastic quantization
scheme are elucidated.Comment: 17 page
- …