Searcharxiv⌕ Search

arXiv subjects

Jean-Paul Blaizot

Publications and source records attributed to Jean-Paul Blaizot.

At least 91 records · Page 5Linked to original sources
arXiv2010

Exact renormalization group and Phi-derivable approximations

We show that the so-called Phi-derivable approximations can be combined with the exact renormalization group to provide efficient non-perturbative approximation schemes. On the one hand, the Phi-derivable approximations allow for a simple truncation of the infinite hierarchy of the renormalization group flow equations. On the other hand, the flow equations turn the non linear equations that derive from the Phi-derivable approximations into an initial value problem, offering new practical ways to solve these equations.

hep-ph↗
arXiv2010

Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group

We apply to the calculation of the pressure of a hot scalar field theory a method that has been recently developed to solve the Non-Perturbative Renormalization Group. This method yields an accurate determination of the momentum dependence of n-point functions over the entire momentum range, from the low momentum, possibly critical, region up to the perturbative, high momentum region. It has therefore the potential to account well for the contributions of modes of all wavelengths to the thermodynamical functions, as well as for the effects of the mixing of quasiparticles with multi-particle states. We compare the thermodynamical functions obtained with this method to those of the so-called Local Potential Approximation, and we find extremely small corrections. This result points to the robustness of the quasiparticle picture in this system. It also demonstrates the stability of the overall approximation scheme, and this up to the largest values of the coupling constant that can be used in a scalar theory in 3+1 dimensions. This is in sharp contrast to perturbation theory which shows no sign of convergence, up to the highest orders that have been recently calculated.

hep-ph↗
arXiv2009

Exact renormalization group at finite temperature

This talk reviews progress in the (semi-) analytic calculations of the thermodynamics of the quark-gluon plasma. I shall explain how weak coupling techniques can allow us, through appropriate resummations, to deal with particular non perturbative aspects of the quark-gluon plasma. Then I shall show how the exact renormalization group may provide insight into the physics of this multi-scale system

hep-ph↗
arXiv2009

Phases of hot and dense QCD matter

This talk summarizes some of the theoretical issues currently most debated in the field of hot and dense QCD matter and ultra-relativistic heavy ion collisions.

hep-ph↗
arXiv2009

Large Nc Confinement, Universal Shocks and Random Matrices

We study the fluid-like dynamics of eigenvalues of the Wilson operator in the context of the order-disorder (Durhuus-Olesen) transition in large $N_c$ Yang-Mills theory. We link the universal behavior at the closure of the gap found by Narayanan and Neuberger to the phenomenon of spectral shock waves in the complex Burgers equation, where the role of viscosity is played by $1/N_c$. Next, we explain the relation between the universal behavior of eigenvalues and certain class of random matrix models. Finally, we conlude the discussion of universality by recalling exact analogies between Yang-Mills theories at large $N_c$ and the so-called diffraction catastrophes.

hep-th↗
arXiv2009

Universal shocks in random matrix theory

We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the case of the Gaussian Unitary Ensemble, on which we focus in this letter, we show that the orthogonal polynomials, and their Cauchy transforms, evolve according to a viscid Burgers equation with an effective "spectral viscosity" $ν_s=1/2N$, where $N$ is the size of the matrices. We relate the edge of the spectrum of eigenvalues to the shock that naturally appears in the Burgers equation for appropriate initial conditions, thereby obtaining a new perspective on universality.

hep-th↗
arXiv2009

Confinement, Turbulence and Diffraction Catastrophes

Many features of large N_c transition that occurs in the spectral density of Wilson loops as a function of loop area (observed recently in numerical simulations of Yang-Mills theory by Narayanan and Neuberger) can be captured by a simple Burgers equation used to model turbulence. Spectral shock waves that precede this asymptotic limit exhibit universal scaling with N_c, with indices that can be related to Berry indices for diffraction catastrophes.

hep-th↗
arXiv2008

The classical field created in early stages of high energy nucleus-nucleus collisions

We show that a special choice of light-cone gauge can greatly simplify the calculation of the classical color field created in the initial stages of nucleus-nucleus collisions. Within this gauge, we can in particular construct explicitly the conserved color current and calculate exactly the gauge field immediately after the collision. This field is used as a boundary condition in an iterative solution of the Yang-Mills equations in the forward light-cone. In leading order, which corresponds to a linearization of the Yang-Mills equation in the forward light-cone, we obtain a simple formula for the spectrum of gluons produced in nucleus-nucleus collisions. This formula reproduces exactly the known formula for proton-nucleus collisions, where $k_t-$factorization is recovered, while the latter property apparently breaks down in the case of nucleus-nucleus collisions.

hep-ph↗
arXiv2008

Large N_c confinement and turbulence

We suggest that the transition that occurs at large $N_c$ in the eigenvalue distribution of a Wilson loop may have a turbulent origin. We arrived at this conclusion by studying the complex-valued inviscid Burgers-Hopf equation that corresponds to the Makeenko-Migdal loop equation, and we demonstrate the appearance of a shock in the spectral flow of the Wilson loop eigenvalues. This picture supplements that of the Durhuus-Olesen transition with a particular realization of disorder. The critical behavior at the formation of the shock allows us to infer exponents that have been measured recently in lattice simulations by Narayanan and Neuberger in $d=2$ and $d=3$. Our analysis leads us to speculate that the universal behavior observed in these lattice simulations might be a generic feature of confinement, also in $d=4$ Yang-Mills theory.

hep-th↗
arXiv2007

Non Perturbative Renormalization Group and Bose-Einstein Condensation

These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature $T_c$ of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have been discussed at this school on effective theories and renormalization group. Effective theories are used first in order to obtain a simple hamiltonian describing the atomic interactions: because the typical atomic interaction potentials are short range, and the systems that we consider are dilute, these potentials can be replaced by a contact interaction whose strength is determined by the s-wave scattering length. Effective theories are used next in order to obtain a simple formula for the shift in $T_c$: one exploits there the fact that near $T_c$ the physics is dominated by low momentum modes whose dynamics is most economically described in terms of classical fields; the ingredients needed to calculate the shift of $T_c$ can be obtained from this classical field theory. Finally the renormalization group is used both to obtain a qualitative understanding, and also as a non perturbative tool to evaluate quantitatively the shift in $T_c$.

cond-mat.stat-mech↗
arXiv2006

High temperature phase of QCD

I give a brief overview of our present understanding of the high temperature phase of QCD, trying to clarify some of the theoretical issues involved in the current discussions that emphasize the strongly coupled character of the quark-gluon plasma produced at RHIC.

nucl-th↗
arXiv2006

Perturbation theory and non-perturbative renormalization flow in scalar field theory at finite temperature

We use the non-perturbative renormalization group to clarify some features of perturbation theory in thermal field theory. For the specific case of the scalar field theory with O(N) symmetry, we solve the flow equations within the local potential approximation. This approximation reproduces the perturbative results for the screening mass and the pressure up to order g^3, and starts to differ at order g^4. The method allows a smooth extrapolation to the regime where the coupling is not small, very similar to that obtained from a simple self-consistent approximation.

hep-ph↗
arXiv2006

Non-Perturbative Renormalization Group calculation of the scalar self-energy

We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow equations for the n-point functions which are also differential equations with respect to a constant background field. This makes them, a priori, difficult to solve. However, we demonstrate in this paper that, within a simple approximation which turns out to be quite accurate, the solution of these flow equations is not more complicated than that of the flow equations obtained in the derivative expansion. Thus, with a numerical effort comparable to that involved in the derivative expansion, we can get the full momentum dependence of the n-point functions. The method is applied, in its leading order, to the calculation of the self-energy in a 3-dimensional scalar field theory, at criticality. Accurate results are obtained over the entire range of momenta.

hep-th↗
arXiv2006

Non perturbative renormalization group and momentum dependence of n-point functions (II)

In a companion paper (hep-th/0512317), we have presented an approximation scheme to solve the Non Perturbative Renormalization Group equations that allows the calculation of the $n$-point functions for arbitrary values of the external momenta. The method was applied in its leading order to the calculation of the self-energy of the O($N$) model in the critical regime. The purpose of the present paper is to extend this study to the next-to-leading order of the approximation scheme. This involves the calculation of the 4-point function at leading order, where new features arise, related to the occurrence of exceptional configurations of momenta in the flow equations. These require a special treatment, inviting us to improve the straightforward iteration scheme that we originally proposed. The final result for the self-energy at next-to-leading order exhibits a remarkable improvement as compared to the leading order calculation. This is demonstrated by the calculation of the shift $ΔT_c$, caused by weak interactions, in the temperature of Bose-Einstein condensation. This quantity depends on the self-energy at all momentum scales and can be used as a benchmark of the approximation. The improved next-to-leading order calculation of the self-energy presented in this paper leads to excellent agreement with lattice data and is within 4% of the exact large $N$ result.

hep-th↗
arXiv2005

The entropy of hot QCD at large N_f: Successfully testing weak coupling techniques

It has been known for some time that the entropy of hot QCD is well reproduced by weak coupling techniques. These do not identify with perturbation theory, known to have poor convergence properties, but involve resumming the physics of hard thermal loops in the non-perturbative Phi-derivable two-loop approximation. We test this approximation scheme in the limit of large flavor number (N_f) where the exact result can be calculated for a wide range of couplings for which the influence of the Landau pole is negligible. Using full momentum-dependent fermionic self-energies instead of the previously only known weighted average value to order g^3, the exact result for the entropy can be remarkably well reproduced by the HTL resummed theory for a natural choice of the renormalization scale, and this up to large values of the coupling. This gives confidence in the reliability of weak coupling techniques when applied to the thermodynamics of QCD, at least for temperatures T > 3 T_c.

hep-ph↗
arXiv2005

Asymptotic thermal quark masses and the entropy of QCD in the large-N_f limit

We study the thermodynamics of QCD in the limit of large flavor number (N_f) and test the proposal to resum the physics of hard thermal loops (HTL) through a nonperturbative expression for the entropy obtained from a Phi-derivable two-loop approximation. The fermionic contribution to the entropy involves a full next-to-leading order evaluation of the asymptotic thermal quark mass, which is non-local, and for which only a weighted average value was known previously. For a natural choice of renormalization scale we find remarkably good agreement of the next-to-leading-order HTL results for the fermion self energy and in turn for the entropy with the respective exact large-N_f results even at very large coupling.

hep-ph↗
arXiv2005

Study of the gluon propagator in the large-N_f limit at finite temperature and chemical potential for weak and strong couplings

At finite temperature and chemical potential, the leading-order (hard-thermal-loop) contributions to the gauge-boson propagator lead to momentum-dependent thermal masses for propagating quasiparticles as well as dynamical screening and Landau damping effects. We compare the hard-thermal-loop propagator with the complete large-N_f gluon propagator, for which the usually subleading contributions, such as a finite width of quasiparticles, can be studied at nonperturbatively large effective coupling. We also study quantitatively the effect of Friedel oscillations in low-temperature electrostatic screening.

hep-ph↗