Non-perturbative renormalization of Phi-derivable approximations in theories with multiple fields

We provide a renormalization procedure for Phi-derivable approximations in theories coupling different types of fields. We illustrate our approach on a scalar phi^4 theory coupled to fermions via a Yukawa-like interaction. The non-perturbative renormalization amounts to fixing the scalar coupling via a set of nested Bethe-Salpeter equations coupling fermions to scalars.Comment: 4 pages, poster contribution at the Workshop on Quark Gluon Plasma Thermalization, Vienna, August 10-12, 2005 Minor changes: added reference and definitio

2PI renormalized effective action for gauge theories

We show how to perform renormalization in the framework of the 2PI effective action for abelian gauge theories. In addition to the usual renormalization conditions one needs to incorporate new ones in order to remove non-transverse UV divergences in the truncated two- and four-photon functions. The corresponding counterterms are allowed by gauge symmetry, in-medium independent and suppressed with respect to the accuracy of the truncation.Comment: 4 pages, to appear in the proceedings of Strong and Electroweak Matter 2006, BNL, New-York, May 200

2PI effective action for gauge theories: Renormalization

We discuss the application of two-particle-irreducible (2PI) functional techniques to gauge theories, focusing on the issue of non-perturbative renormalization. In particular, we show how to renormalize the photon and fermion propagators of QED obtained from a systematic loop expansion of the 2PI effective action. At any finite order, this implies introducing new counterterms as compared to the usual ones in perturbation theory. We show that these new counterterms are consistent with the 2PI Ward identities and are systematically of higher order than the approximation order, which guarantees the convergence of the approximation scheme. Our analysis can be applied to any theory with linearly realized gauge symmetry. This is for instance the case of QCD quantized in the background field gauge.Comment: 21 pages, 8 figures. Uses JHEP3.cl

A critical look at the role of the bare parameters in the renormalization of Phi-derivable approximations

We revisit the renormalization of Phi-derivable approximations from a slightly different point of view than the one which is usually followed in previous works. We pay particular attention to the question of the existence of a solution to the self-consistent equation that defines the two-point function in the Cornwall-Jackiw-Tomboulis formalism and to the fact that some of the ultraviolet divergences which appear if one formally expands the solution in powers of the bare coupling do not always appear as divergences at the level of the solution itself. We discuss these issues using a particular truncation of the Phi functional, namely the simplest truncation which brings non-trivial momentum and field dependence to the two-point function.Comment: 30 pages, 12 figure

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

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

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

Yang-Mills correlators across the deconfinement phase transition

We compute the finite temperature ghost and gluon propagators of Yang-Mills theory in the Landau-DeWitt gauge. The background field that enters the definition of the latter is intimately related with the (gauge-invariant) Polyakov loop and serves as an equivalent order parameter for the deconfinement transition. We use an effective gauge-fixed description where the nonperturbative infrared dynamics of the theory is parametrized by a gluon mass which, as argued elsewhere, may originate from the Gribov ambiguity. In this scheme, one can perform consistent perturbative calculations down to infrared momenta, which have been shown to correctly describe the phase diagram of Yang-Mills theories in four dimensions as well as the zero-temperature correlators computed in lattice simulations. In this article, we provide the one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon propagators for a large class of gauge groups and present explicit results for the SU(2) case. These are substantially different from those previously obtained in the Landau gauge, which corresponds to a vanishing background field. The nonanalyticity of the order parameter across the transition is directly imprinted onto the propagators in the various color modes. In the SU(2) case, this leads, for instance, to a cusp in the electric and magnetic gluon susceptibilities as well as similar signatures in the ghost sector. We mention the possibility that such distinctive features of the transition could be measured in lattice simulations in the background field gauge studied here.Comment: 28 pages, 17 figures; published versio

2PI functional techniques for abelian gauge theories

We summarize our recent work [1-3] concerning the formulation of two-particle-irreducible (2PI) functional techniques for abelian gauge field theories.Comment: To appear in the proceedings of SEWM08, Amsterdam, The Netherlands, 26-29 August 200

Broken phase scalar effective potential and Phi-derivable approximations

We study the effective potential of a real scalar phi(4) theory as a function of the temperature T within the simplest Phi-derivable approximation, namely, the Hartree approximation. We apply renormalization at a "high" temperature T(star) where the theory is required to be in its symmetric phase and study how the effective potential evolves as the temperature is lowered down to T = 0. In particular, we prove analytically that no second order phase transition can occur in this particular approximation of the theory, in agreement with earlier studies based on the numerical evaluation or the high temperature expansion of the effective potential. This work is also an opportunity to illustrate certain issues on the renormalization of Phi-derivable approximations at finite temperature and nonvanishing field expectation value and to introduce new computational techniques which might also prove useful when dealing with higher order approximations