Bosonization and Functional Renormalization Group Approach in the Framework of QED_2

Known results on two-dimensional quantum electrodynamics (QED_2) have been used to study the dependence of functional renormalization group equations on renormalization schemes and approximations applied for its bosonized version. It is demonstrated that the singularity of flow equations can be avoided in the optimized and power-law schemes for the bosonized model and the drawback of renormalization on bosonization is shown: it is indicated that renormalization of QED_2 possibly requires interaction terms corresponding to higher frequency modes of its bosonized version.Comment: v3: 8 pages, 7 figures, final version, published in Phys. Rev.

Periodic Higgs, Inflaton, Axion Potentials and the Sine-Gordon Universality Class

Higgs, inflaton and axion physics are examples where scalar fields naturally appear, in the two former cases, usually with a polynomial type self-interaction. In this work possible applications of periodic scalar potentials are discussed which belong to the sine-Gordon universality class. For example, a periodic self-interaction is proposed here as a possible extension, UV completion of the standard model Higgs potential. Using the usual parametrisation of the field around the first minimum, one recovers the Lagrangian of the Higgs sector but with a periodic interaction term for a single-component real scalar field. Another possible application is inflationary cosmology where the so called natural inflation i.e., the periodic PNGB potential has already been used as a competing inflationary model. Finally, one has to mention the periodic axion potential which was proposed to retain the CP conserving nature of QCD where, in principle, gauge symmetry and renormalizability allow the inclusion of CP violating terms but experimental data do not favour such an extension. The purpose of this work is to map out the exact phase structure of the sine-Gordon model by the functional renormalization group (RG) method in arbitrary dimension and to study the consequences of its renormalization on Higgs, inflaton and axion physics. It is shown that the pure sine-Gordon model has a single (broken) phase for d>2. Results are used to study the phase structure of the equivalent neutral Coulomb gas and to demonstrate that the isotropic XY spin model belongs to a different universality class for d>2. The findings (i) open a new platform to perform stability studies for models with periodic type Higgs potential which can be used as a possible UV completion, (ii) clarify the role of the RG running of the frequency parameter in the PNGB inflationary model, (iii) confirm the flattening of the axion potential.Comment: 14 pages, 6 figure

Renormalization of QCD_2

The low energy infrared scaling of the multi-color 2-dimensional quantum chromodynamics is determined in the framework of its bosonized model by using the functional renormalization group method with gliding sharp cut-off k in momentum space in the local potential approximation. The model exhibits a single phase with a superuniversal effective potential.Comment: 15 pages, 3 figures, final versio

Neutrino Splitting for Lorentz-Violating Neutrinos: Detailed Analysis

Lorentz-violating neutrino parameters have been severely constrained on the basis of astrophysical considerations. In the high-energy limit, one generally assumes a superluminal dispersion relation of an incoming neutrino of the form E ~ |p|v, where E is the energy, p is the momentum and $v = sqrt(1 + delta) > 1. Lepton-pair creation due to a Cerenkov-radiation-like process (nu -> nu + e^- + e^+) becomes possible above a certain energy threshold, and bounds on the Lorentz-violating parameter delta can be derived. Here, we investigate a related process, nu_i -> nu_i + nu_f + bar_nu_f, where nu_i is an incoming neutrino mass eigenstate, while nu_f is the final neutrino mass eigenstate, with a superluminal velocity that is slightly slower than that of the initial state. This process is kinematically allowed if the Lorentz-violating parameters at high energy differ for the different neutrino mass eigenstates. Neutrino splitting is not subject to any significant energy threshold condition and could yield quite a substantial contribution to decay and energy loss processes at high energy, even if the differential Lorentz violation among neutrino flavors is severely constrained by other experiments. We also discuss the SU(2)-gauge invariance of the superluminal models and briefly discuss the use of a generalized vierbein formalism in the formulation of the Lorentz-violating Dirac equation.Comment: 17 pages; RevTeX; to appear in Physical Review

Gravitational Interactions and Fine-Structure Constant

Electromagnetic and gravitational central-field problems are studied with relativistic quantum mechanics on curved space-time backgrounds. Corrections to the transition current are identified. Analogies of the gravitational and electromagnetic spectra suggest the definition of a gravitational fine-structure constant. The electromagnetic and gravitational coupling constants enter the Einstein-Hilbert-Maxwell Lagrangian. We postulate that the variational principle holds with regard to a global dilation transformation of the space-time coordinates. The variation suggests is consistent with a functional relationship of the form alpha_QED being proportional to alpha_G^(1/2), where alpha_QED is the electrodynamic fine-structure constant, and alpha_G its gravitational analogue.Comment: 9 pages; LaTeX; Appeared in the Proceedings to the 17th Bled workshop "What Comes Beyond the Standard Models", Bled, Slovenia, July 2-28, 2014; Editors N. S. Mankoc Borstnik, H. B. Nielsen and D. Lukman; ISSN 1580-4992; book series: Bled Workshops in Physics vol. 15, no. 2, pp. 115-122 (2014

Renormalization-Group Analysis of the Generalized sine-Gordon Model and of the Coulomb Gas for d >= 3 Dimensions

Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d >= 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d >= 3, independent of the dimensionality, and in sharp contrast to the special case d = 2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations), that the blocked potential tends to a constant effective potential in the infrared (IR) limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used.Comment: 19 pages, 8 figure

Renormalization of the Periodic Scalar Field Theory by Polchinski's Renormalization Group Method

The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this work we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas.Comment: 14 pages, LaTeX, 1 figure; J. Phys. G (in press