585 research outputs found
Wilsonian flows and background fields
We study exact renormalisation group flows for background field dependent
regularisations. It is shown that proper-time flows are approximations to exact
background field flows for a specific class of regulators. We clarify the role
of the implicit scale dependence introduced by the background field. Its impact
on the flow is evaluated numerically for scalar theories at criticality for
different approximations and regularisations. Implications for gauge theories
are discussed.Comment: 12 pages, v2: references added. to appear in PL
Subleading critical exponents from the renormalisation group
We study exact renormalisation group equations for the 3d Ising universality
class. At the Wilson-Fisher fixed point, symmetric and antisymmetric
correction-to-scaling exponents are computed with high accuracy for an
optimised cutoff to leading order in the derivative expansion. Further results
are derived for other cutoffs including smooth, sharp and background field
cutoffs. An estimate for higher order corrections is given as well. We
establish that the leading antisymmetric corrections to scaling are strongly
subleading compared to the leading symmetric ones.Comment: 10 pages, 5 figure
Critical exponents from optimised renormalisation group flows
Within the exact renormalisation group, the scaling solutions for O(N)
symmetric scalar field theories are studied to leading order in the derivative
expansion. The Gaussian fixed point is examined for d>2 dimensions and
arbitrary infrared regularisation. The Wilson-Fisher fixed point in d=3 is
studied using an optimised flow. We compute critical exponents and subleading
corrections-to-scaling to high accuracy from the eigenvalues of the stability
matrix at criticality for all N. We establish that the optimisation is
responsible for the rapid convergence of the flow and polynomial truncations
thereof. The scheme dependence of the leading critical exponent is analysed.
For all N > 0, it is found that the leading exponent is bounded. The upper
boundary is achieved for a Callan-Symanzik flow and corresponds, for all N, to
the large-N limit. The lower boundary is achieved by the optimised flow and is
closest to the physical value. We show the reliability of polynomial
approximations, even to low orders, if they are accompanied by an appropriate
choice for the regulator. Possible applications to other theories are outlined.Comment: 34 pages, 15 figures, revtex, to appear in NP
Fixed points of quantum gravity in extra dimensions
We study quantum gravity in more than four dimensions with renormalisation
group methods. We find a non-trivial ultraviolet fixed point in the
Einstein-Hilbert action. The fixed point connects with the perturbative
infrared domain through finite renormalisation group trajectories. We show that
our results for fixed points and related scaling exponents are stable. If this
picture persists at higher order, quantum gravity in the metric field is
asymptotically safe. We discuss signatures of the gravitational fixed point in
models with low-scale gravity and compact extra dimensions.Comment: Wording sharpened, refs added, to appear in PL
Gauge invariance and background field formalism in the exact renormalisation group
We discuss gauge symmetry and Ward-Takahashi identities for Wilsonian flows
in pure Yang-Mills theories. The background field formalism is used for the
construction of a gauge invariant effective action. The symmetries of the
effective action under gauge transformations for both the gauge field and the
auxiliary background field are separately evaluated. We examine how the
symmetry properties of the full theory are restored in the limit where the
cut-off is removed.Comment: version to be published in PL
Aspects of semi-classical transport theory for QCD
We discuss some aspects of a recently proposed semi-classical transport
theory for QCD plasmas based on coloured point particles. This includes the
derivation of effective transport equations for mean fields and fluctuations
which relies on the Gibbs ensemble average. Correlators of fluctuations are
interpreted as collision integrals for the effective Boltzmann equation. The
approach yields a recipe to integrate-out fluctuations. Systematic
approximations (first moment, second moment, polarisation approximation) based
on a small plasma parameter are discussed as well. Finally, the application to
a hot non-Abelian plasma close to thermal equilibrium is considered and the
consistency with the fluctuation-dissipation theorem established.Comment: Presented at Strong and Electroweak Matter (SEWM2000), Marseille,
France, 14-17 June 2000, 12 page
Renormalization-Group flow for the field strength in scalar self-interacting theories
We consider the Renormalization-Group coupled equations for the effective
potential V(\phi) and the field strength Z(\phi) in the spontaneously broken
phase as a function of the infrared cutoff momentum k. In the k \to 0 limit,
the numerical solution of the coupled equations, while consistent with the
expected convexity property of V(\phi), indicates a sharp peaking of Z(\phi)
close to the end points of the flatness region that define the physical
realization of the broken phase. This might represent further evidence in favor
of the non-trivial vacuum field renormalization effect already discovered with
variational methods.Comment: 10 pages, 3 Figures, version accepted for publication in Phys. Lett.
Derivative expansion and renormalisation group flows
We study the convergence of the derivative expansion for flow equations. The
convergence strongly depends on the choice for the infrared regularisation.
Based on the structure of the flow, we explain why optimised regulators lead to
better physical predictions. This is applied to O(N)-symmetric real scalar
field theories in 3d, where critical exponents are computed for all N. In
comparison to the sharp cut-off regulator, an optimised flow improves the
leading order result up to 10%. An analogous reasoning is employed for a proper
time renormalisation group. We compare our results with those obtained by other
methods.Comment: 15 pages, 5 figure
Transport theory and low energy properties of colour superconductors
The one-loop polarisation tensor and the propagation of ``in-medium'' photons
of colour superconductors in the 2SC and CFL phase is discussed. For a study of
thermal corrections to the low energy effective theory in the 2SC phase, a
classical transport theory for fermionic quasiparticles is invoked.Comment: 5 pages, talk given at the International Conference on "Statistical
QCD", Bielefeld, August 26-30, 200
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