arXiv subjects

Holger Gies

Publications and source records attributed to Holger Gies.

At least 145 records · Page 8Linked to original sources

arXiv2004

Renormalization flow of QED

We investigate textbook QED in the framework of the exact renormalization group. In the strong-coupling region, we study the influence of fluctuation-induced photonic and fermionic self-interactions on the nonperturbative running of the gauge coupling. Our findings confirm the triviality hypothesis of complete charge screening if the ultraviolet cutoff is sent to infinity. Though the Landau pole does not belong to the physical coupling domain owing to spontaneous chiral symmetry breaking (chiSB), the theory predicts a scale of maximal UV extension of the same order as the Landau pole scale. In addition, we verify that the chiSB phase of the theory which is characterized by a light fermion and a Goldstone boson also has a trivial Yukawa coupling.

hep-ph↗

arXiv2003

Towards a renormalizable standard model without fundamental Higgs scalar

We investigate the possibility of constructing a renormalizable standard model with purely fermionic matter content. The Higgs scalar is replaced by point-like fermionic self-interactions with couplings growing large at the Fermi scale. An analysis of the UV behavior in the point-like approximation reveals a variety of non-Gaussian fixed points for the fermion couplings. If real, such fixed points would imply nonperturbative renormalizability and evade triviality of the Higgs sector. For point-like fermionic self-interactions and weak gauge couplings, one encounters a hierarchy problem similar to the one for a fundamental Higgs scalar.

hep-ph↗

arXiv2003

Universality of spontaneous chiral symmetry breaking in gauge theories

We investigate one-flavor QCD with an additional chiral scalar field. For a large domain in the space of coupling constants, this model belongs to the same universality class as QCD, and the effects of the scalar become unobservable. This is connected to a ``bound-state fixed point'' of the renormalization flow for which all memory of the microscopic scalar interactions is lost. The QCD domain includes a microscopic scalar potential with minima at nonzero field. On the other hand, for a scalar mass term m^2 below a critical value m_c^2, the universality class is characterized by perturbative spontaneous chiral symmetry breaking which renders the quarks massive. Our renormalization group analysis shows how this universality class is continuously connected with the QCD universality class.

hep-th↗

arXiv2003

Casimir Effect on the Worldline

We develop a method to compute the Casimir effect for arbitrary geometries. The method is based on the string-inspired worldline approach to quantum field theory and its numerical realization with Monte-Carlo techniques. Concentrating on Casimir forces between rigid bodies induced by a fluctuating scalar field, we test our method with the parallel-plate configuration. For the experimentally relevant sphere-plate configuration, we study curvature effects quantitatively and perform a comparison with the ``proximity force approximation'', which is the standard approximation technique. Sizable curvature effects are found for a distance-to-curvature-radius ratio of a/R >~ 0.02. Our method is embedded in renormalizable quantum field theory with a controlled treatment of the UV divergencies. As a technical by-product, we develop various efficient algorithms for generating closed-loop ensembles with Gaussian distribution.

hep-th↗

arXiv2003

Renormalizability of gauge theories in extra dimensions

We analyze the possibility of nonperturbative renormalizability of gauge theories in D > 4 dimensions. We develop a scenario, based on Weinberg's idea of asymptotic safety, that allows for renormalizability in extra dimensions owing to a non-Gaussian ultraviolet stable fixed point. Our scenario predicts a critical dimension D_cr beyond which the UV fixed point vanishes, such that renormalizability is possible for D <= D_cr. Within the framework of exact RG equations, the critical dimension for various SU(N) gauge theories can be computed to lie near five dimensions: 5 ~< D_cr < 6. Therefore, our results exclude nonperturbative renormalizability of gauge theories in D=6 and higher dimensions.

hep-th↗

arXiv2002

Zero modes, beta functions and IR/UV interplay in higher-loop QED

We analyze the relation between the short-distance behavior of quantum field theory and the strong-field limit of the background field formalism, for QED effective Lagrangians in self-dual backgrounds, at both one and two loop. The self-duality of the background leads to zero modes in the case of spinor QED, and these zero modes must be taken into account before comparing the perturbative beta function coefficients and the coefficients of the strong-field limit of the effective Lagrangian. At one-loop this is familiar from instanton physics, but we find that at two-loop the role of the zero modes, and the interplay between IR and UV effects in the renormalization, is quite different. Our analysis is motivated in part by the remarkable simplicity of the two-loop QED effective Lagrangians for a self-dual constant background, and we also present here a new independent derivation of these two-loop results.

hep-th↗

arXiv2002

Fermion-induced quantum action of vortex systems

The quantum action generated by fermions which are minimally coupled to abelian vortex background fields is studied in D=2+1 and D=3+1 Euclidean dimensions. We present a detailed analysis of single- and binary-vortex configurations using the recently developed method of worldline numerics. The dependence of the fermion-induced quantum action on the fermion mass and the magnetic fluxes carried by the vortices is studied, and the binary-vortex interaction is computed. Additionally, we discuss the chiral condensate generated from a dilute gas of vortices in the intermediate fermion mass range for the case D=3+1. As a byproduct, our findings provide insight into the validity limits of the derivative expansion, which is the standard analytical approach to inhomogeneous backgrounds.

hep-th↗

arXiv2002

Renormalization flow from UV to IR degrees of freedom

Within the framework of exact renormalization group flow equations, a scale-dependent transformation of the field variables provides for a continuous translation of UV to IR degrees of freedom. Using the gauged NJL model as an example, this translation results in a construction of partial bosonization at all scales. A fixed-point structure arises which makes it possible to distinguish between fundamental-particle and bound-state behavior of the scalar fields.

hep-ph↗

arXiv2002

Running coupling in Yang-Mills theory - a flow equation study -

The effective average action of Yang-Mills theory is analyzed in the framework of exact renormalization group flow equations. Employing the background-field method and using a cutoff that is adjusted to the spectral flow, the running of the gauge coupling is obtained on all scales. In four dimensions and for the gauge groups SU(2) and SU(3), the coupling approaches a fixed point in the infrared.

hep-th↗

arXiv2001

Loops and loop clouds - a numerical approach to the worldline formalism in QED -

A numerical technique for calculating effective actions of electromagnetic backgrounds is proposed, which is based on the string-inspired worldline formalism. As examples, we consider scalar electrodynamics in three and four dimensions to one-loop order. Beyond the constant-magnetic-field case, we analyze a step-function-like magnetic field exhibiting a nonlocal and nonperturbative phenomenon: ``magnetic-field diffusion''. Finally, generalizations to fermionic loops and systems at finite temperature are discussed.

hep-ph↗

arXiv2001

Renormalization Flow of Bound States

A renormalization group flow equation with a scale-dependent transformation of field variables gives a unified description of fundamental and composite degrees of freedom. In the context of the effective average action, we study the renormalization flow of scalar bound states which are formed out of fundamental fermions. We use the gauged Nambu--Jona-Lasinio model at weak gauge coupling as an example. Thereby, the notions of bound state or fundamental particle become scale dependent, being classified by the fixed-point structure of the flow of effective couplings.

hep-th↗

arXiv2001

QED Effective Action Revisited

The derivation of a convergent series representation for the quantum electrodynamic effective action obtained by two of us (S.R.V. and D.R.L.) in [Can. J. Phys. vol. 71, p. 389 (1993)] is reexamined. We present more details of our original derivation. Moreover, we discuss the relation of the electric-magnetic duality to the integral representation for the effective action, and we consider the application of nonlinear convergence acceleration techniques which permit the efficient and reliable numerical evaluation of the quantum correction to the Maxwell Lagrangian.

hep-th↗

arXiv2001

Quantum diffusion of magnetic fields in a numerical worldline approach

We propose a numerical technique for calculating effective actions of electromagnetic backgrounds based on the worldline formalism. As a conceptually simple example, we consider scalar electrodynamics in three dimensions to one-loop order. Beyond the constant-magnetic-field case, serving as a benchmark test, we analyze the effective action of a step-function-like magnetic field -- a configuration that is inaccessible to derivative expansions. We observe magnetic-field diffusion, i.e., nonvanishing magnetic action density at space points near the magnetic step where the classical field vanishes.

hep-ph↗

arXiv2001

Wilsonian effective action for SU(2) Yang-Mills theory with Cho-Faddeev-Niemi-Shabanov decomposition

The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is employed for the calculation of the corresponding Wilsonian effective action to one-loop order with covariant gauge fixing. The generation of a mass scale is observed, and the flow of the marginal couplings is studied. Our results indicate that higher-derivative terms of the color-unit-vector $\mathbf{n}$ field are necessary for the description of topologically stable knotlike solitons which have been conjectured to be the large-distance degrees of freedom.

hep-th↗

arXiv2001

Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part III

The string-inspired technique is used for a first calculation of the one-loop axialvector vacuum polarisation in a general constant electromagnetic field. A compact result is reached for the difference between this tensor and the corresponding vector vacuum polarisation. This result is confirmed by a Feynman diagram calculation. Its physical relevance is briefly discussed.

hep-ph↗

arXiv2001

Flow equation for Halpern-Huang directions of scalar O(N) models

A class of asymptotically free scalar theories with O(N) symmetry, defined via the eigenpotentials of the Gaussian fixed point (Halpern-Huang directions), are investigated using renormalization group flow equations. Explicit solutions for the form of the potential in the nonperturbative infrared domain are found in the large-N limit. In this limit, potentials without symmetry breaking essentially preserve their shape and undergo a mass renormalization which is governed only by the renormalization group distance parameter; as a consequence, these scalar theories do not have a problem of naturalness. Symmetry-breaking potentials are found to be ``fine-tuned'' in the large-N limit in the sense that the nontrivial minimum vanishes exactly in the limit of vanishing infrared cutoff: therefore, the O(N) symmetry is restored in the quantum theory and the potential becomes flat near the origin.

hep-th↗

arXiv2000

Effective action for the order parameter of the deconfinement transition of Yang-Mills theories

The effective action for the Polyakov loop serving as an order parameter for deconfinement is obtained in one-loop approximation to second order in a derivative expansion. The calculation is performed in $d\geq 4$ dimensions, mostly referring to the gauge group SU(2). The resulting effective action is only capable of describing a deconfinement phase transition for $d>d_{\text{cr}}\simeq 7.42$. Since, particularly in $d=4$, the system is strongly governed by infrared effects, it is demonstrated that an additional infrared scale such as an effective gluon mass can change the physical properties of the system drastically, leading to a model with a deconfinement phase transition.

hep-th↗

arXiv2000

From effective actions to actual effects in QED

The construction of low-energy effective actions in QED for several types of external conditions is reviewed. Emphasis is put on the application of these effective actions to a variety of physical effects which represent a manifestation of vacuum polarization. Soft-photon interactions with external electromagnetic fields and/or a heat bath are described, pair production at finite temperature is discussed, and finally a glance at photon-neutrino interactions is provided.

hep-ph↗