43 research outputs found
Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
We study the confinement-deconfinement phase transition of pure Yang-Mills
theories at finite temperature using a simple massive extension of standard
background field methods. We generalize our recent next-to-leading-order
perturbative calculation of the Polyakov loop and of the related background
field effective potential for the SU(2) theory to any compact and connex Lie
group with a simple Lie algebra. We discuss in detail the SU(3) theory, where
the two-loop corrections yield improved values for the first-order transition
temperature as compared to the one-loop result. We also show that certain
one-loop artifacts of thermodynamical observables disappear at two-loop order,
as was already the case for the SU(2) theory. In particular, the entropy and
the pressure are positive for all temperatures. Finally, we discuss the groups
SU(4) and Sp(2) which shed interesting light, respectively, on the relation
between the (de)confinement of static matter sources in the various
representations of the gauge group and on the use of the background field
itself as an order parameter for confinement. In both cases, we obtain
first-order transitions, in agreement with lattice simulations and other
continuum approaches.Comment: 35 pages, 20 figure
Yang-Mills correlators at finite temperature: A perturbative perspective
We consider the two-point correlators of Yang-Mills theories at finite
temperature in the Landau gauge. We employ a model for the corresponding
Yang-Mills correlators based on the inclusion of an effective mass term for
gluons. The latter is expected to have its origin in the existence of Gribov
copies. One-loop calculations at zero temperature have been shown to agree
remarkably well with the corresponding lattice data. We extend on this and
perform a one-loop calculation of the Matsubara gluon and ghost two-point
correlators at finite temperature. We show that, as in the vacuum, an effective
gluon mass accurately captures the dominant infrared physics for the magnetic
gluon and ghost propagators. It also reproduces the gross qualitative features
of the electric gluon propagator. In particular, we find a slight nonmonotonous
behavior of the Debye mass as a function of temperature, however not as
pronounced as in existing lattice results. A more quantitative description of
the electric sector near the deconfinement phase transition certainly requires
another physical ingredient sensitive to the order parameter of the transition.Comment: 16 pages, 12 figures ; Published version (PRD
Deconfinement transition in SU(N) theories from perturbation theory
We consider a simple massive extension of the Landau-DeWitt gauge for SU()
Yang-Mills theory. We compute the corresponding one-loop effective potential
for a temporal background gluon field at finite temperature. At this order the
background field is simply related to the Polyakov loop, the order parameter of
the deconfinement transition. Our perturbative calculation correctly describes
a quark confining phase at low temperature and a phase transition of second
order for and weakly first order for . Our estimates for the
transition temperatures are in qualitative agreement with values from lattice
simulations or from other continuum approaches. Finally, we discuss the
effective gluon mass parameter in relation to the Gribov ambiguities of the
Landau-DeWitt gauge.Comment: 10 pages, 3 figure
Branching rate expansion around annihilating random walks
We present some exact results for branching and annihilating random walks. We
compute the nonuniversal threshold value of the annihilation rate for having a
phase transition in the simplest reaction-diffusion system belonging to the
directed percolation universality class. Also, we show that the accepted
scenario for the appearance of a phase transition in the parity conserving
universality class must be improved. In order to obtain these results we
perform an expansion in the branching rate around pure annihilation, a theory
without branching. This expansion is possible because we manage to solve pure
annihilation exactly in any dimension.Comment: 5 pages, 5 figure
Superfluidity within Exact Renormalisation Group approach
The application of the exact renormalisation group to a many-fermion system
with a short-range attractive force is studied. We assume a simple ansatz for
the effective action with effective bosons, describing pairing effects and
derive a set of approximate flow equations for the effective coupling including
boson and fermionic fluctuations.
The phase transition to a phase with broken symmetry is found at a critical
value of the running scale. The mean-field results are recovered if boson-loop
effects are omitted. The calculations with two different forms of the regulator
was shown to lead to similar results.Comment: 17 pages, 3 figures, to appear in the proceedings of Renormalization
Group 2005 (RG 2005), Helsinki, Finland, 30 Aug - 3 Sep 200
Massive Yang-Mills Theory in Abelian Gauges
We prove the perturbative renormalisability of pure SU(2) Yang-Mills theory
in the abelian gauge supplemented with mass terms. Whereas mass terms for the
gauge fields charged under the diagonal U(1) allow to preserve the standard
form of the Slavnov-Taylor identities (but with modified BRST variations), mass
terms for the diagonal gauge fields require the study of modified
Slavnov-Taylor identities. We comment on the renormalization group equations,
which describe the variation of the effective action with the different masses.
Finite renormalized masses for the charged gauge fields, in the limit of
vanishing bare mass terms, are possible provided a certain combination of wave
function renormalization constants vanishes sufficiently rapidly in the
infrared limit.Comment: added explanations, corrected sign
An Infrared Safe perturbative approach to Yang-Mills correlators
We investigate the 2-point correlation functions of Yang-Mills theory in the
Landau gauge by means of a massive extension of the Faddeev-Popov action. This
model is based on some phenomenological arguments and constraints on the
ultraviolet behavior of the theory. We show that the running coupling constant
remains finite at all energy scales (no Landau pole) for and argue that
the relevant parameter of perturbation theory is significantly smaller than 1
at all energies. Perturbative results at low orders are therefore expected to
be satisfactory and we indeed find a very good agreement between 1-loop
correlation functions and the lattice simulations, in 3 and 4 dimensions.
Dimension 2 is shown to play the role of an upper critical dimension, which
explains why the lattice predictions are qualitatively different from those in
higher dimensions.Comment: 16 pages, 7 figures, accepted for publication in PR
Convergence of random zeros on complex manifolds
We show that the zeros of random sequences of Gaussian systems of polynomials
of increasing degree almost surely converge to the expected limit distribution
under very general hypotheses. In particular, the normalized distribution of
zeros of systems of m polynomials of degree N, orthonormalized on a regular
compact subset K of C^m, almost surely converge to the equilibrium measure on K
as the degree N goes to infinity.Comment: 16 page
A nonequilibrium renormalization group approach to turbulent reheating
We use nonequilibrium renormalization group (RG) techniques to analyze the
thermalization process in quantum field theory, and by extension reheating
after inflation. Even if at a high scale the theory is described by a
non-dissipative theory, the RG running induces nontrivial
noise and dissipation. For long wavelength, slowly varying field
configurations, the noise and dissipation are white and ohmic, respectively.
The theory will then tend to thermalize to an effective temperature given by
the fluctuation-dissipation theorem.Comment: 8 pages, 2 figures; to appear in J. Phys. A; more detailed account of
the calculation of the noise and dissipation kernel
Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion
With a view to study the convergence properties of the derivative expansion
of the exact renormalization group (RG) equation, I explicitly study the
leading and next-to-leading orders of this expansion applied to the
Wilson-Polchinski equation in the case of the -vector model with the
symmetry . As a test, the critical exponents and as well as the subcritical exponent (and higher ones) are estimated
in three dimensions for values of ranging from 1 to 20. I compare the
results with the corresponding estimates obtained in preceding studies or
treatments of other exact RG equations at second order. The
possibility of varying allows to size up the derivative expansion method.
The values obtained from the resummation of high orders of perturbative field
theory are used as standards to illustrate the eventual convergence in each
case. A peculiar attention is drawn on the preservation (or not) of the
reparametrisation invariance.Comment: Dedicated to Lothar Sch\"afer on the occasion of his 60th birthday.
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