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($N$) 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 $N=2$ and weakly first order for $N=3$. 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 $d>2$ 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 $\Lambda$ the theory is described by a non-dissipative $\lambda\phi^{4}$ 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 $N$-vector model with the symmetry $\mathrm{O}(N)$. As a test, the critical exponents $$ and $\nu$ as well as the subcritical exponent $\omega$ (and higher ones) are estimated in three dimensions for values of $N$ ranging from 1 to 20. I compare the results with the corresponding estimates obtained in preceding studies or treatments of other $\mathrm{O}(N)$ exact RG equations at second order. The possibility of varying $N$ 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. Final versio