Kai Schwenzer

QCD and strongly coupled gauge theories: challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement

The infrared behavior of the quark–gluon vertex of quenched Landau gauge QCD is studied by analyzing its Dyson Schwinger equation. Building on previously obtained results for Green functions in the Yang–Mills sector, we analytically derive the existence of powerlawinfrared singularities for this vertex.Weestablish that dynamical chiral symmetry breaking leads to the self-consistent generation of components of the quark–gluon vertex forbidden when chiral symmetry is forced to stay in the Wigner–Weyl mode. In the latter case the running strong coupling assumes an infrared fixed point. If chiral symmetry is broken, eitherdynamically orexplicitly, the running coupling is infrared divergent. Based on a truncation for the quark–gluon vertex Dyson–Schwinger equation which respects the analytically determined infrared behavior, numerical results for the coupled system of the quark propagator and vertex Dyson–Schwinger equation are presented. The resulting quarkmass function aswell as the vertex function show only a very weak dependence on the current quark mass in the deep infrared. From this we infer by an analysis of the quark–quark scattering kernel a linearly rising quark potential with analmostmass independent string tensionin the case of brokenchiral symmetry. Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore, we conclude that chiral symmetry breaking and confinement are closely related. Furthermore, we discuss aspects of confinement as the absence of long range van derWaals forces and Casimir scaling. An examination of experimental data for quarkonia provides further evidence for the viability of the presented mechanism for quark confinement in the Landau gauge.

Infrared singularities in Landau gauge Yang-Mills theory

We present a more detailed picture of the infrared regime of Landau-gauge Yang-Mills theory. This is done within a novel framework that allows one to take into account the influence of finite scales within an infrared power counting analysis. We find that there are two qualitatively different infrared fixed points of the full system of Dyson-Schwinger equations. The first extends the known scaling solution, where the ghost dynamics is dominant and gluon propagation is strongly suppressed. It features in addition to the strong divergences of gluonic vertex functions in the previously considered uniform scaling limit, when all external momenta tend to zero, also weaker kinematic divergences, when only some of the external momenta vanish. The second solution represents the recently proposed decoupling scenario where the gluons become massive and the ghosts remain bare. In this case we find that none of the vertex functions is enhanced, so that the infrared dynamics is entirely suppressed. Our analysis also provides a strict argument why the Landau-gauge gluon dressing function cannot be infrared divergent.

The infrared behavior of Landau gauge Yang–Mills theory in d=2, 3 and 4 dimensions

Abstract We develop a general power counting scheme for the infrared limit of Landau gauge SU ( N ) Yang–Mills theory in arbitrary dimensions. Employing a skeleton expansion, we find that the infrared behavior is qualitatively independent of the spacetime dimension d . In the cases d = 2 , 3 and 4 even the quantitative results for the infrared exponents of the vertices differ only slightly. Therefore, corresponding lattice simulations provide interesting qualitative information for the physical case. We furthermore find that the loop integrals depend only weakly on the numerical values of the IR exponents.

Algorithmic derivation of Dyson–Schwinger equations ☆

Abstract We present an algorithm for the derivation of Dyson–Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE 1 which provides such an implementation. It derives the Dyson–Schwinger equations graphically once the interactions of the theory are specified. A few examples for the application of both the algorithm and the DoDSE package are provided. Program summary Program title: DoDSE Catalogue identifier: AECT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECT_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 105 874 No. of bytes in distributed program, including test data, etc.: 262 446 Distribution format: tar.gz Programming language: Mathematica 6 and higher Computer: all on which Mathematica is available Operating system: all on which Mathematica is available Classification: 11.1, 11.4, 11.5, 11.6 Nature of problem: Derivation of Dyson–Schwinger equations for a theory with given interactions. Solution method: Implementation of an algorithm for the derivation of Dyson–Schwinger equations. Unusual features: The results can be plotted as Feynman diagrams in Mathematica. Running time: Less than a second to minutes for Dyson–Schwinger equations of higher vertex functions.

On the infrared scaling solution of SU(N) Yang-Mills theories in the maximally Abelian gauge

An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang–Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared divergent scaling solution possible for vertex functions in terms of the propagators’ infrared exponents. We provide general conditions for the existence of a scaling solution for a given system and comment on the cases of linear covariant gauges and ghost–anti-ghost symmetric gauges.

Linking the quark meson model with QCD at high temperature

We model the transition of a system of quarks and gluons at high energies to a system of quarks and mesons at low energies in a consistent renormalization group approach. Flow equations interpolate between the physics of the high-temperature degrees of freedom and the low-temperature dynamics at a scale of 1 GeV. We also discuss the dependence of the equation of state on baryon density and compare our results with recent lattice gauge simulations.

Non-Fermi liquid effects in QCD at high density

We study non-Fermi liquid effects due to the exchange of unscreened magnetic gluons in the normal phase of high density QCD by using an effective field theory. A one-loop calculation gives the well-known result that magnetic gluons lead to a logarithmic enhancement in the fermion self-energy near the Fermi surface. The self-energy is of the form {sigma}({omega}){approx}{omega}{gamma}log({omega}), where {omega} is the energy of the fermion, {gamma}=O(g{sup 2}), and g is the coupling constant. Using an analysis of the Dyson-Schwinger equations we show that, in the weak coupling limit, this result is not modified by higher order corrections even in the regime where the logarithm is large, {gamma}log({omega}){approx}1. We also show that this result is consistent with the renormalization group equation in the high density effective field theory.

Gravitational wave emission and spin-down of young pulsars

The rotation frequencies of young pulsars are systematically below their theoretical Kepler limit. R-modes have been suggested as a possible explanation for this observation. With the help of semi-analytic expressions that make it possible to assess the uncertainties of the r-mode scenario due to the impact of uncertainties in underlying microphysics, we perform a quantitative analysis of the spin-down and the emitted gravitational waves of young pulsars. We find that the frequency to which r-modes spin down a young neutron star is surprisingly insensitive both to the microscopic details and the saturation amplitude. Comparing our result to astrophysical data, we show that for a range of sufficiently large saturation amplitudes r-modes provide a viable spindown scenario and that all observed young pulsars are very likely already outside the r-mode instability region. Therefore the most promising sources for gravitational wave detection are unobserved neutron stars associated with recent supernovae, and we find that advanced LIGO should be able to see several of them. We find the remarkable result that the gravitational wave strain amplitude is completely independent of both the r-mode saturation amplitude and the microphysics, and depends on the saturation mechanism only within some tens of per cent. However, the gravitational wave frequency depends on the amplitude and we provide the required expected timing parameter ranges to look for promising sources in future searches.

QCD and strongly coupled gauge theories

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.