arXiv subjects
Publications and source records attributed to Julien Serreau.
We address the lattice computation of the gluon propagator in the center-symmetric Landau gauge. After discussing a proper lattice implementation of the center-symmetric Landau gauge, we compare the lattice data with analytical results, and we identify various signatures of center symmetry breaking.
A lattice implementation of the recently introduced center-symmetric Landau gauge is discussed and its predictions confronted with numerical Monte Carlo simulations. It is shown that the link average and the link correlators computed in that gauge are order parameters of the confinement-deconfinement transition at nonzero temperature. Strictly speaking, this requires a specific treatment of the Gribov copies that we discuss in detail. The numerical simulations comply with the theoretical predictions for the link average computed below and above the deconfinement temperature. Our results show that, within appropriately chosen gauges, one can construct local order parameters for center symmetry, as proxies for the non-local Polyakov loop.
We revisit the non-Abelian dipole problem in the context of a simple semiclassical approach that incorporates some essential features of the infrared sector of Yang-Mills theories in the Landau gauge, in particular, the fact that both the running coupling and the gluon propagator remain finite at infrared scales and that the latter shows positivity violations that reflects the presence of massless modes. We obtain a simple flux tube solution in a controlled approximation scheme, which we compare to the results of lattice simulations.
We continue our investigation of the QCD dynamics in terms of the Curci-Ferrari effective Lagrangian, a deformation of the Faddeev-Popov one in the Landau gauge with a tree-level gluon mass term. In a previous work we have studied the dynamics of chiral symmetry breaking at the level of the quark propagator and, in particular, the dynamical generation of a constituent quark mass. In the present article, we study the associated Goldstone mode, the pion, and we compute the pion decay constant in the chiral limit. Our approach exploits the fact that the coupling (defined in the Taylor scheme) in the pure gauge sector is perturbative, as observed in lattice simulations which, together with a $1/N_c$-expansion, allows for a systematic, controllable approximation scheme in the low energy regime of QCD. At leading order, this leads to the well-known rainbow-ladder resummation. We study the region of parameter space of the model that gives physical values of the pion decay constant. This allows one to constrain the gluon mass parameter as a function of the coupling using a physically measured quantity.
Lattice simulations of the QCD correlation functions in the Landau gauge have established two remarkable facts. First, the coupling constant in the gauge sector remains finite and moderate at all scales, suggesting that some kind of perturbative description should be valid down to infrared momenta. Second, the gluon propagator reaches a finite nonzero value at vanishing momentum, corresponding to a gluon screening mass. We review recent studies which aim at describing the long-distance properties of Landau gauge QCD by means of the perturbative Curci-Ferrari model. The latter is the simplest deformation of the Faddeev-Popov Lagrangian in the Landau gauge that includes a gluon screening mass at tree-level. There are, by now, strong evidences that this approach successfully describes many aspects of the infrared QCD dynamics. In particular, several correlation functions were computed at one- and two-loop orders and compared with {\it ab-initio} lattice simulations. The typical error is of the order of ten percent for a one-loop calculation and drops to few percents at two loops. We review such calculations in the quenched approximation as well as in the presence of dynamical quarks. In the latter case, the spontaneous breaking of the chiral symmetry requires to go beyond a coupling expansion but can still be described in a controlled approximation scheme in terms of small parameters. We also review applications of the approach to nonzero temperature and chemical potential.
We propose a novel approach to the confinement-deconfinement transition in Yang-Mills theories in the context of gauge-fixed calculations. The method is based on a background-field generalisation of the Landau gauge (to which it reduces at vanishing temperature) with a given, center-symmetric background. This is to be contrasted with most implementations of background field methods in gauge theories, where one uses a variable, self-consistent background. Our proposal is a bona fide gauge fixing that can easily be implemented on the lattice and in continuum approaches. The resulting gauge-fixed action explicitly exhibits the center symmetry of the nonzero temperature theory that controls the confinement-deconfinement transition. We show that, in that gauge, the electric susceptibility diverges at a second order transition [e.g., in the SU(2) theory], so that the gluon propagator is a clear probe of the transition. We implement our proposal in the perturbative Curci-Ferrari model, known for its successful description of various infrared aspects of Yang-Mills theories, including the confinement-deconfinement transition. Our one-loop calculation confirms our general expectation for the susceptibility while providing transition temperatures in excellent agreement with the SU(2) and SU(3) lattice values. Finally, the Polyakov loops above the transition show a more moderate rise, in contrast to previous implementations of the Curci-Ferrari model using a self-consistent background, and our SU(3) result agrees quite well with lattice results in the range $[0,2T_c]$.
We investigate the spontaneous breaking of chiral symmetry in QCD by means of a recently proposed approximation scheme in the Landau-gauge Curci-Ferrari model, which combines an expansion in the Yang-Mills coupling and in the inverse number of colors, without expanding in the quark-gluon coupling. The expansion allows for a consistent treatment of ultraviolet tails via renormalization group techniques. At leading order, it leads to the resummation of rainbow diagrams for the quark propagator, with, however, a trivial running of both the gluon mass and the quark-gluon coupling. In a previous work, by using a simple model for a more realistic running of these parameters, we could reproduce the known phenomenology of chiral symmetry breaking, including a satisfactory description of the lattice data for the quark mass function. Here, we get rid of this model-dependence by taking our approximation scheme to next-to-leading order. This allows us to consistently include the realistic running of the parameters and to access the unquenched gluon and ghost propagators to first nontrivial order, which we can compare to available lattice data for an even more stringent test of our approach. In particular, our results for the various two-point functions compare well with lattice data while the parameters of the model are strongly constrained.
We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.
We study the phase diagram of strongly interacting matter with light quarks using a recently proposed, small parameter approach to infrared QCD in the Landau gauge. This is based on an expansion with respect to both the inverse number of colors and the pure Yang-Mills coupling in the presence of a Curci-Ferrari mass term. At leading order, this leads to the well-known rainbow equation for the quark propagator with a massive gluon propagator. We solve the latter at nonzero temperature and chemical potential using a simple semi-analytic approximation known to capture the essence of chiral symmetry breaking in the vacuum. In the chiral limit, we find a tricritical point which becomes a critical endpoint in the presence of a nonzero bare quark mass, in agreement with the results of nonperturbative functional methods and model calculations. This supports the view that the present approach allows for a systematic study of the QCD phase diagram in a controlled expansion scheme.
The flavor dependence of the QCD phase diagram presents universal properties in the heavy quark limit. For the wide class of models where the quarks are treated at the one-loop level, we show, for arbitrary chemical potential, that the flavor dependence of the critical quark masses-for which the confinement-deconfinement transition is second order-is insensitive to the details of the (confining) gluon dynamics and that the critical temperature is constant along the corresponding critical line. We illustrate this with explicit results in various such one-loop models studied in the literature: effective matrix models for the Polyakov loop, the Curci-Ferrari model, and a recently proposed Gribov-Zwanziger-type model. We further observe that the predictions which follow from this one-loop universality property are well satisfied by different calculations beyond one-loop order, including lattice simulations. For degenerate quarks, we propose a simple universal law for the flavor dependence of the critical mass, satisfied by all approaches.
We study the backreaction of superhorizon fluctuations of a light quantum scalar field on a classical de Sitter geometry by means of the Wilsonian renormalisation group. This allows us to treat the gravitationally amplified fluctuations in a nonperturbative manner and to analytically follow the induced renormalisation flow of the spacetime curvature as long wavelength modes are progressively integrated out. Unbounded loop corrections in the deep infrared are eventually screened by nonperturbative effects which stabilise the geometry.
We study the long-distance properties of quantum chromodynamics in an expansion in powers of the three-gluon, four-gluon, and ghost-gluon couplings, but without expanding in the quark-gluon coupling. This is motivated by two observations. First, the gauge sector is well-described by perturbation theory in the context of a phenomenological model with a massive gluon. Second, the quark-gluon coupling is significantly larger than those in the gauge sector at large distances. In order to resum the contributions of the remaining infinite set of QED-like diagrams, we further expand the theory in $1/N_c$, where $N_c$ is the number of colors. At leading order, this double expansion leads to the well-known rainbow approximation for the quark propagator. We take advantage of the systematic expansion to get a renormalization-group improvement of the rainbow resummation. A simple numerical solution of the resulting coupled set of equations reproduces the phenomenology of the spontaneous chiral symmetry breaking: for sufficiently large quark-gluon coupling constant, the constituent quark mass saturates when its valence mass approaches zero. We find very good agreement with lattice data for the scalar part of the propagator and explain why the vectorial part is poorly reproduced.
We study the Landau gauge correlators of Yang-Mills fields for infrared Euclidean momenta in the context of a massive extension of the Faddeev-Popov Lagrangian which, we argue, underlies a variety of continuum approaches. Standard (perturbative) renormalization group techniques with a specific, infrared-safe renormalization scheme produce so-called decoupling and scaling solutions for the ghost and gluon propagators, which correspond to nontrivial infrared fixed points. The decoupling fixed point is infrared stable and weakly coupled, while the scaling fixed point is unstable and generically strongly coupled except for low dimensions $d\to2$. Under the assumption that such a scaling fixed point exists beyond one-loop order, we find that the corresponding ghost and gluon scaling exponents are, respectively, $2α_F=2-d$ and $2α_G=d$ at all orders of perturbation theory in the present renormalization scheme. We discuss the relation between the ghost wave function renormalization, the gluon screening mass, the scale of spectral positivity violation, and the gluon mass parameter. We also show that this scaling solution does not realize the standard Becchi-Rouet-Stora-Tyutin symmetry of the Faddeev-Popov Lagrangian. Finally, we discuss our findings in relation to the results of nonperturbative continuum methods.
Nonperturbative renormalization group techniques have recently proven a powerful tool to tackle the nontrivial infrared dynamics of light scalar fields in de Sitter space. In the present article, we develop the formalism beyond the local potential approximation employed in earlier works. In particular, we consider the derivative expansion, a systematic expansion in powers of field derivatives, appropriate for long wavelength modes, that we generalize to the relevant case of a curved metric with Lorentzian signature. The method is illustrated with a detailed discussion of the so-called local potential approximation prime which, on top of the full effective potential, includes a running (but field-independent) field renormalization. We explicitly compute the associated anomalous dimension for O(N) theories. We find that it can take large values along the flow, leading to sizable differences as compared to the local potential approximation. However, it does not prevent the phenomenon of gravitationally induced dimensional reduction pointed out in previous studies. We show that, as a consequence, the effective potential at the end of the flow is unchanged as compared to the local potential approximation, the main effect of the running anomalous dimension being merely to slow down the flow.
We study the dynamics of light quantum scalar fields in de Sitter space on superhorizon scales. We compute the self-energy of an O(N) symmetric theory at next-to-leading order in a 1/N expansion in the regime of superhorizon momenta, and we obtain an exact analytical solution of the corresponding Dyson-Schwinger equations for the two-point correlator. This amounts to resumming the infinite series of nonlocal self-energy insertions, which typically generate spurious infrared and/or secular divergences. The potentially large de Sitter logarithms resum into well-behaved power laws from which we extract the field strength and mass renormalization. The nonperturbative 1/N expansion allows us to discuss the case of vanishing and negative tree-level square mass, which both correspond to strongly coupled effective theories in the infrared.
We consider Yang-Mills theories in a recently proposed family of nonlinear covariant gauges that consistently deals with the issue of Gribov ambiguities. Such gauges provide a generalization of the Curci-Ferrari-Delbourgo-Jarvis gauges which can be formulated as an extremization procedure and might be implemented in numerical calculations. This would allow for nonperturbative studies of Yang-Mills correlators in a broad class of covariant gauges continuously connected to the well-studied Landau gauge. We compute the ghost and gluon propagators in the continuum formulation at one-loop order in perturbation theory and we study their momentum dependence down to the deep infrared regime, with and without renormalization group improvement. In particular, we show that the theory admits infrared-safe renormalization-group trajectories with no Landau pole. Both the gluon and the ghost behave as massive fields at low energy, and the gluon propagator is transverse even away from the Landau gauge limit. We compare our results to those obtained in the usual Curci-Ferrari model, which allows us to pinpoint the specific effects arising from our treatment of Gribov copies.
We investigate scalar field theories in de Sitter space by means of nonperturbative renormalization group techniques. We compute the functional flow equation for the effective potential of O(N) theories in the local potential approximation and we study the onset of curvature-induced effects as quantum fluctuations are progressively integrated out from subhorizon to superhorizon scales. This results in a dimensional reduction of the original action to an effective zero-dimensional Euclidean theory. We show that the latter is equivalent both to the late-time equilibrium state of the stochastic approach of Starobinsky and Yokoyama and to the effective theory for the zero mode on Euclidean de Sitter space. We investigate the immediate consequences of this dimensional reduction: symmetry restoration and dynamical mass generation.
We investigate the phase diagram of QCD with heavy quarks at finite temperature and chemical potential in the context of background field methods. In particular, we use a massive extension of the Landau-DeWitt gauge which is motivated by previous studies of the deconfinement phase transition in pure Yang-Mills theories. We show that a simple one-loop calculation is able to capture the richness of the phase diagram in the heavy quark region, both at real and imaginary chemical potential. Moreover, dimensionless ratios of quantities directly measurable in numerical simulations are in good agreement with lattice results.