Finiteness of the Coulomb gauge QCD perturbative effective action

At 2-loop order in the Coulomb gauge, individual Feynman graphs contributing to the effective action have energy divergences. It is proved that these cancel in suitable combinations of graphs. This has previously been shown only for transverse external fields. The calculation results in a generalization of the Christ–Lee term which was inserted into the Hamiltonian.     

Convergence of Feynman integrals in Coulomb gauge QCD

At 2-loop order, Feynman integrals in the Coulomb gauge are divergent over the internal energy variables. Nevertheless, it is known how to calculate the effective action, provided that the external gluon fields are all transverse. We show that, for the two-gluon Greens function as an example, the method can be extended to include longitudinal external fields. The longitudinal Greens functions appear in the BRST identities. As an intermediate step, we use a flow gauge, which interpolates between the Feynman and Coulomb gauges.     

Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation

We review and extend in several directions recent results on the “asymptotic safety” approach to quantum gravity. The central issue in this approach is the search of a Fixed Point having suitable properties, and the tool that is used is a type of Wilsonian renormalization group equation. We begin by discussing various cutoff schemes, i.e. ways of implementing the Wilsonian cutoff procedure. We compare the beta functions of the gravitational couplings obtained with different schemes, studying first the contribution of matter fields and then the so-called Einstein-Hilbert truncation, where only the cosmological constant and Newton’s constant are retained. In this context we make connection with old results, in particular we reproduce the results of the epsilon expansion and the perturbative one-loop divergences. We then apply the Renormalization Group to higher derivative gravity. In the case of a general action quadratic in curvature we recover, within certain approximations, the known asymptotic freedom of the four-derivative terms, while Newton’s constant and of the cosmological constant have a nontrivial fixed point. In the case of actions that are polynomials in the scalar curvature of degree up to eight we find that the theory has a fixed point with three UV-attractive directions, so that the requirement of having a continuum limit constrains the couplings to lie in a three-dimensional subspace, whose equation is explicitly given. We emphasize throughout the difference between scheme-dependent and scheme-independent results, and provide several examples of the fact that only dimensionless couplings can have “universal” behavior.     

Quantum gravitational contributions to the beta function of quantum electrodynamics

We show in a diagrammatic and regularization independent analysis that the quadratic contribution to the beta function which has been conjectured to render quantum electrodynamics asymptotically free near the Planck scale has its origin in a surface term. Such surface term is intrinsically arbitrarily valued and it is argued to vanish in a consistent treatment of the model.     

Evaluating results from the Relativistic Heavy Ion Collider with perturbative QCD and hydrodynamics

We review the basic concepts of perturbative quantum chromodynamics (QCD) and relativistic hydrodynamics, and their applications to hadron production in high energy nuclear collisions. We discuss results from the Relativistic Heavy Ion Collider (RHIC) in light of these theoretical approaches. Perturbative QCD and hydrodynamics together explain a large amount of experimental data gathered during the first decade of RHIC running, although some questions remain open. We focus primarily on practical aspects of the calculations, covering basic topics like perturbation theory, initial state nuclear effects, jet quenching models, ideal hydrodynamics, dissipative corrections, freeze-out and initial conditions. We conclude by comparing key results from RHIC to calculations.     

Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.     

Study of the spectral properties of spin ladders in different representations via a renormalization procedure

We implement an algorithm which is aimed to reduce the dimensions of the Hilbert space of quantum many-body systems by means of a renormalization procedure. We test the role and importance of different representations on the reduction process by working out and analyzing the spectral properties of strongly interacting frustrated quantum spin systems.     

Instability of the plasma oscillations in finite temperature perturbative QCD

We use linear-response dielectric theory to show that the baryon-poor QCD plasma based on the perturbative vacuum is unstable, even at a high temperature. If deconfinement occurs in nuclear collisions or the early universe, it is not accompanied by the restoration of the perturbative vacuum.     

Emergence of mass in the gauge sector of QCD

It is currently widely accepted that gluons, while massless at the level of the fundamental QCD Lagrangian, acquire an effective mass through the non-Abelian implementation of the classic Schwinger mechanism. The key dynamical ingredient that triggers the onset of this mechanism is the formation of composite massless poles inside the fundamental vertices of the theory. These poles enter the evolution equation of the gluon propagator and nontrivially affect the way the Slavnov-Taylor identities of the vertices are resolved, inducing a smoking-gun displacement in the corresponding Ward identities. In this article, we present a comprehensive review of the pivotal concepts associated with this dynamical scenario, emphasizing the synergy between functional methods and lattice simulations and highlighting recent advances that corroborate the action of the Schwinger mechanism in QCD.     

QCD Dirac spectrum and components of the gauge field

We analyze the relation between the Dirac spectrum and the gauge field in SU(3) lattice QCD. We focus on how a certain component of the gauge field is related to the Dirac spectrum. First, we consider momentum components of the gauge field. It turns out that the broad momentum region is relevant for the low-lying Dirac spectrum and topological charges. The connection with chiral random matrix theory is also discussed. Second, we consider an SU(2) subgroup component of the SU(3) gauge field. The SU(2) subgroup component behaves like the SU(2) gauge field in the low-lying Dirac spectrum.     

Quantum fluctuations and the Kondo effect in small quantum dots

We consider electron transport through quantum dots with large level spacing and charging energy. At low temperature and strong coupling to the leads, quantum fluctuations and the Kondo effect become important. They show up, e.g., as zero-bias anomalies in the current–voltage characteristics. We use a recently developed diagrammatic technique as well as a new real-time renormalization-group approach to describe charge and spin fluctuations. The latter gives rise to a Kondo-assisted enhancement of the current through the dot as seen in experiments.     

Leading logarithms in the anomalous sector of two-flavour QCD

We add the Wess–Zumino–Witten term to the N=3$N=3$ massive nonlinear sigma model and study the leading logarithms in the anomalous sector. We obtain the leading logarithms to six loops for π⁰→γ^?γ^?${\pi }^0\to {\gamma }^{?}{\gamma }^{?}$ and to five loops for γ^?πππ${\gamma }^{?}\pi \pi \pi$. In addition we extend the earlier work on the mass and decay constant to six loops and the vector form factor to five loops. We present numerical results for the anomalous processes and the vector form factor. In all cases the series are found to converge rapidly.     

The space-time picture of the Wee partons and the AGK cutting rules in perturbative QCD

We discuss the space-time picture of scattering amplitudes with single and double ladder exchange in perturbative QCD. Particular emphasis is given to the Abramovsky Gribov Kanchelli (AGK) rules which describe the relative contributions of the diffractive dissociation and processes with other multiplicities to the elastic scattering amplitude. Inside the Pomeron Pomeron interaction vertices we find a new matrix which describes the transition from one s-cut to another and which goes beyond the original AGK rules.     

Rigorous Proof of Luttinger Liquid Behavior in the 1d Hubbard Model

We give the first rigorous (non perturbative) proof of Luttinger liquid behavior in the one dimensional Hubbard model, for small repulsive interaction and values of the density different from half filling. The analysis is based on the combination of multiscale analysis with Ward identities based on a hidden and approximate local chiral gauge invariance. No use is done of exact solutions or special integrability properties of the Hubbard model, and the results can be in fact easily generalized to include non local interactions, magnetic fields or interaction with external potentials     

Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model

The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions. In the present study, we determine the pole structure of pion–nucleon scattering in an analytic model based on meson exchange. For this, the sheet structure of the amplitude is determined. To show the precision of the resonance extraction and discuss phenomena such as resonance interference, we discuss the S₁₁ amplitude in greater detail.     

Localization length exponent,critical conductance distribution and multifractality in hierarchical network models for the quantum Hall effect

We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 5 (1997) 1422; Arovas et al., PRB 56 (1997) 4751). The hierarchical structure is due to a recursive method starting from a finite elementary cell. The localization-delocalization transition occurring in these models is displayed in the flow of the conductance distribution under increasing system size. We numerically determine this flow, calculate the critical conductance distribution, the critical exponent of the localization length, and the multifractal exponents of critical eigenstates.