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

Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles $n(p)\sim p^{-\nu}$ with exponent $\nu\simeq 2$, which is larger than expected from relativistic $2\leftrightarrow 2$ scatterings. Using the approach of Zakharov, L'vov and Falkovich, we analyse possible Kolmogorov coefficients for relativistic $(m \ge 4)$-particle processes, which give at most $\nu=5/3$ perturbatively for an energy cascade. We discuss nonperturbative scenarios which lead to larger values. As an extreme limit we find the result $\nu=5$ generically in an inherently nonperturbative effective field theory situation, which coincides with results obtained by Berges et al.\ in large-$N$ scalar field theory. If we instead assume that scaling behavior is determined by Schwinger-Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario which would single out $\nu=2$.Comment: published versio

EMMI Rapid Reaction Task Force on "Thermalization in Non-abelian Plasmas"

Recently, different proposals have been put forward on how thermalization proceeds in heavy-ion collisions in the idealized limit of very large nuclei at sufficiently high energy. Important aspects of the parametric estimates at weak coupling may be tested using well-established classical-statistical lattice simulations of the far-from-equilibrium gluon dynamics. This has to be confronted with strong coupling scenarios in related theories based on gauge-string dualities. Furthermore, closely related questions about far-from-equilibrium dynamics arise in early-universe cosmology and in non-relativistic systems of ultracold atoms. These were central topics of the EMMI Rapid Reaction Task Force meeting held on December 12-14, 2011, at the University of Heidelberg, which we report on.Comment: 13 pages, summary of the EMMI Rapid Reaction Task Force on "Thermalization in Non-abelian Plasmas", December 12-14, 2011, University of Heidelberg, German

Functional renormalization for Bose-Einstein Condensation

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For three dimensional dilute gases, we find an upper bound on the scattering length a which is of the order of the microphysical scale - typically the range of the Van der Waals interaction. In contrast to fermions near the unitary bound, no strong interactions occur for bosons with approximately pointlike interactions, thus explaining the high quantitative reliability of perturbation theory for most quantities. For zero temperature we compute the quantum phase diagram for bosonic quasiparticles with a general dispersion relation, corresponding to an inverse microphysical propagator with terms linear and quadratic in the frequency. We compute the temperature dependence of the condensate and particle density n, and find for the critical temperature T_c a deviation from the free theory, Delta T_c/T_c = 2.1 a n^{1/3}. For the sound velocity at zero temperature we find very good agreement with the Bogoliubov result, such that it may be used to determine the particle density accurately.Comment: 21 pages, 16 figures. Reference adde

Functional renormalization for trion formation in ultracold fermion gases

The energy spectrum for three species of identical fermionic atoms close to a Feshbach resonance is computed by use of a nonperturbative flow equation. Already a simple truncation shows that for large scattering length $|a|$ the lowest energy state is a "trion" (or trimer) bound state of three atoms. At the location of the resonance, for $|a|\to\infty$, we find an infinite set of trimer bound states, with exponentially decreasing binding energy. This feature was pointed out by Efimov. It arises from limit cycle scaling, which also leads to a periodic dependence of the three body scattering coupling on $\ln |a|$. Extending our findings by continuity to nonzero density and temperature we find that a "trion phase" separates a BEC and a BCS phase, with interesting quantum phase transitions for T=0.Comment: 9 pages, 4 figures, minor changes, reference adde

2PI Effective Action and Evolution Equations of N = 4 super Yang-Mills

We employ nPI effective action techniques to study N = 4 super Yang-Mills, and write down the 2PI effective action of the theory. We also supply the evolution equations of two-point correlators within the theory.Comment: 16 pages, 6 figures. Figure 2 replaced, approximation scheme clarified, references adde

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}[\phi], 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.Comment: 33 pages, 2 figure

Transport coefficients from the 2PI effective action

We show that the lowest nontrivial truncation of the two-particle irreducible (2PI) effective action correctly determines transport coefficients in a weak coupling or 1/N expansion at leading (logarithmic) order in several relativistic field theories. In particular, we consider a single real scalar field with cubic and quartic interactions in the loop expansion, the O(N) model in the 2PI-1/N expansion, and QED with a single and many fermion fields. Therefore, these truncations will provide a correct description, to leading (logarithmic) order, of the long time behavior of these systems, i.e. the approach to equilibrium. This supports the promising results obtained for the dynamics of quantum fields out of equilibrium using 2PI effective action techniques.Comment: 5 pages, explanation in introduction expanded, summary added; to appear in PR

Critical Opalescence in Baryonic QCD Matter

We show that critical opalescence, a clear signature of second-order phase transition in conventional matter, manifests itself as critical intermittency in QCD matter produced in experiments with nuclei. This behaviour is revealed in transverse momentum spectra as a pattern of power laws in factorial moments, to all orders, associated with baryon production. This phenomenon together with a similar effect in the isoscalar sector of pions (sigma mode) provide us with a set of observables associated with the search for the QCD critical point in experiments with nuclei at high energies.Comment: 7 pages, 1 figur