Searcharxiv⌕ Search

arXiv subjects

J. Serreau

Publications and source records attributed to J. Serreau.

At least 19 recordsLinked to original sources
arXiv2020

The $1/N$ expansion for stochastic fields in de Sitter spacetime

We propose a $1/N$ expansion of Starobinsky and Yokoyama's effective stochastic approach for light quantum fields on superhorizon scales in de Sitter spacetime. We explicitly compute the spectrum and the eigenfunctions of the Fokker-Planck operator for a O($N$)-symmetric theory with quartic selfinteraction at leading and next-to-leading orders in this expansion. We obtain simple analytical expressions valid in various nonperturbative regimes in terms of the interaction coupling constant.

hep-th↗
arXiv2020

Unequal time correlators of stochastic scalar fields in de Sitter space

The quantum fluctuations of a test scalar field on superhorizon scale in de Sitter spacetime can be described by an effective one-dimensional stochastic theory corresponding to a particular class of nonequilibrium dynamical systems known as the model A. Using the formulation of the latter in terms of a supersymmetric field theory, we compute various unequal-time correlators at large (superhorizon) time separations and compare with existing quantum field theory computation. This includes perturbative calculations, pushed here up to three-loop order, and a nonperturbative $1/N$ expansion at next-to-leading order. Exploiting the supersymmetry of the stochastic theory, we also derive a spectral representation of the field correlators and a fluctuation-dissipation relation for the infrared modes of the scalar field in de Sitter spacetime.

hep-th↗
arXiv2018

Backreaction of superhorizon scalar field fluctuations on a de Sitter geometry : a renormalisation group perspective

We study the backreaction of gravitationally amplified quantum fluctuations of scalar fields on a classical de Sitter geometry. We formulate the problem in the framework of the Wilsonian renormalisation group, which allows us to treat the scalar field fluctuations in a nonperturbative manner and to follow the renormalisation flow of the spacetime curvature as long wavelength, superhorizon fluctuations are progressively integrated out. For light fields in units of the spacetime curvature, these are described by an effective zero-dimensional field theory and can essentially be computed analytically. A nontrivial flow of the spacetime curvature is induced either by a nonminimal coupling to gravity or by self-interactions. The latter leads to a decrease of the spacetime curvature through loop effects, which, for minimally coupled, massless fields, grow unbounded in the infrared. However, such large loop contributions are eventually screened by the dynamical generation of a nonperturbative, gravitationally induced mass and the renormalisation of the spacetime curvature saturates to a nonzero value. Finally, we show that, in the case of spontaneously broken continuous symmetries, the Goldstone modes do not contribute to the infrared flow of the spacetime curvature, despite being strongly amplified by the gravitational field.

hep-th↗
arXiv2017

A perturbative study of the QCD phase diagram for heavy quarks at nonzero chemical potential: two-loop corrections

We extend a previous investigation of the QCD phase diagram with heavy quarks in the context of background field methods by including the two-loop corrections to the background field effective potential. The nonperturbative dynamics in the pure-gauge sector is modeled by a phenomenological gluon mass term in the Landau-DeWitt gauge-fixed action, which results in an improved perturbative expansion. We investigate the phase diagram at nonzero temperature and (real or imaginary) chemical potential. Two-loop corrections yield an improved agreement with lattice data as compared to the leading-order results. We also compare with the results of nonperturbative approaches. We further study the equation of state as well as the thermodynamic stability of the system at two-loop order. Finally, we show, using simple thermodynamic arguments, that the behavior of the Polyakov loops as functions of the chemical potential complies with their interpretation in terms of quark and anti-quark free energies.

hep-ph↗
arXiv2017

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.

hep-th↗
arXiv2016

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.

hep-th↗
arXiv2015

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.

hep-ph↗
arXiv2015

Deconfinement transition in SU(2) Yang-Mills theory: A two-loop study

In a recent work we have proposed a perturbative approach for the study of the phase transition of pure Yang-Mills theories at finite temperature. This is based on a simple massive extension of background field methods in the Landau-DeWitt gauge, where the gluon mass term is related to the existence of Gribov ambiguities. We have shown that a one-loop calculation of the background field effective potential describes well the phase structure of the SU(2) and SU(3) theories. Here, we present the calculation of the next-to-leading-order contribution in perturbation theory for the SU(2) case. In particular, we compute the background field effective potential at two-loop order and the corresponding Polyakov loop, a gauge invariant order parameter of the transition, at one-loop order. We show that the two-loop correction brings the critical temperature closer to its actual value as compared to the previous one-loop result. We also compute the thermodynamic pressure as a function of the temperature and show that two-loop contributions play an important role in the vicinity of the phase transition.

hep-th↗
arXiv2014

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.

hep-th↗
arXiv2013

Physical momentum representation of scalar field correlators in de Sitter space

We propose a new approach to compute correlators of quantum fields in de Sitter space. It is based on nonequilibrium field theory techniques, and exploits de Sitter symmetries so as to partially reduce the number of independent variables of n-point functions in a manner that preserves the usefulness of a momentum representation, e.g., for writing spatial convolution integrals as simple products. In this representation, the two-point function of a scalar field only depends on two physical momenta, and the corresponding Schwinger-Dyson evolution equations take the form of momentum flow equations. Moreover, standard diagrammatic rules can be entirely formulated in this representation. The method is suitable for analytical approximations as well as numerical implementations. In forthcoming publications, we apply it to resum infrared logarithmic terms appearing in the perturbative calculation of vertex and correlation functions.

hep-th↗
arXiv2011

Quantum properties of a non-Gaussian state in the large-N approximation

We study the properties of a non-Gaussian density matrix for a O(N) scalar field in the context of the incomplete description picture. This is of relevance for studies of decoherence and entropy production in quantum field theory. In particular, we study how the inclusion of the simplest non-Gaussian correlator in the set of measured observables modifies the effective (Gaussian) description one can infer from the knowledge of the two-point functions only. We compute exactly the matrix elements of the non-Gaussian density matrix at leading order in a 1/N-expansion. This allows us to study the quantum properties (purity, entropy, coherence) of the corresponding state for arbitrarily strong nongaussianity. We find that if the Gaussian and the non-Gaussian observers essentially agree concerning quantum purity or correlation entropy, their conclusion can significantly differ for other, more detailed aspects such as the degree of quantum coherence of the system.

quant-ph↗
arXiv2009

2PI functional techniques for gauge theories: QED

We discuss the formulation of the prototype gauge field theory, QED, in the context of two-particle-irreducible (2PI) functional techniques with particular emphasis on the issues of renormalization and gauge symmetry. We show how to renormalize all $n$-point vertex functions of the (gauge-fixed) theory at any approximation order in the 2PI loop-expansion by properly adjusting a finite set of local counterterms consistent with the underlying gauge symmetry. The paper is divided in three parts: a self-contained presentation of the main results and their possible implementation for practical applications; a detailed analysis of ultraviolet divergences and their removal; a number of appendices collecting technical details.

hep-ph↗
arXiv2008

Ward Identities for the 2PI effective action in QED

We study the issue of symmetries and associated Ward-like identities in the context of two-particle-irreducible (2PI) functional techniques for abelian gauge theories. In the 2PI framework, the $n$-point proper vertices of the theory can be obtained in various different ways which, although equivalent in the exact theory, differ in general at finite approximation order. We derive generalized (2PI) Ward identities for these various $n$-point functions and show that such identities are exactly satisfied at any approximation order in 2PI QED. In particular, we show that 2PI-resummed vertex functions, i.e. field-derivatives of the so-called 2PI-resummed effective action, exactly satisfy standard Ward identities. We identify another set of $n$-point functions in the 2PI framework which exactly satisfy the standard Ward identities at any approximation order. These are obtained as field-derivatives of the two-point function $\bcG^{-1}[ϕ]$, which defines the extremum of the 2PI effective action. We point out that the latter is not constrained by the underlying symmetry. As a consequence, the well-known fact that the corresponding gauge-field polarization tensor is not transverse in momentum space for generic approximations does not constitute a violation of (2PI) Ward identities. More generally, our analysis demonstrates that approximation schemes based on 2PI functional techniques respect all the Ward identities associated with the underlying abelian gauge symmetry. Our results apply to arbitrary linearly realized global symmetries as well.

hep-th↗
arXiv2005

Renormalized thermodynamics from the 2PI effective action

High-temperature resummed perturbation theory is plagued by poor convergence properties. The problem appears for theories with bosonic field content such as QCD, QED or scalar theories. We calculate the pressure as well as other thermodynamic quantities at high temperature for a scalar one-component field theory, solving a three-loop 2PI effective action numerically without further approximations. We present a detailed comparison with the two-loop approximation. One observes a strongly improved convergence behavior as compared to perturbative approaches. The renormalization employed in this work extends previous prescriptions, and is sufficient to determine all counterterms required for the theory in the symmetric as well as the spontaneously broken phase.

hep-ph↗
arXiv2004

Photon Physics in Heavy Ion Collisions at the LHC

Various pion and photon production mechanisms in high-energy nuclear collisions at RHIC and LHC are discussed. Comparison with RHIC data is done whenever possible. The prospect of using electromagnetic probes to characterize quark-gluon plasma formation is assessed.

hep-ph↗
arXiv2003

Parametric resonance in quantum field theory

We present the first study of parametric resonance in quantum field theory from a complete next-to-leading order calculation in a 1/N-expansion of the 2PI effective action, which includes scattering and memory effects. We present a complete numerical solution for an O(N)-symmetric scalar theory and provide an approximate analytic description of the nonlinear dynamics in the entire amplification range. We find that the classical resonant amplification at early times is followed by a collective amplification regime with explosive particle production in a broad momentum range, which is not accessible in a leading-order calculation.

hep-ph↗