Renormalization group equations for effective field theories

We derive the renormalization group equations for a generic non-renormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral perturbation theory, e.g., this means that one can obtain the series of leading chiral logs by calculating only one-loop diagrams. We discuss also the renormalization group equations for the subleading divergences, and the crucial role of counterterms that vanish at the equations of motion. Finally, we show that the renormalization group equations obtained here apply equally well also to renormalizable theories.Received: 5 September 2003, Published online: 20 November 2003     

Renormalization group evolution of the CKM matrix

We compute the renormalization of the complete CKM matrix in the scheme and perform a renormalization group analysis of the CKM parameters. The calculation is simplified by studying only the Higgs sector, which for the -function of the CKM matrix is at one loop the same as in the full Standard Model. The renormalization group flow including QCD corrections can be computed analytically using the hierarchy of the CKM parameters and the large mass differences between the quarks. While the evolution of the Cabibbo angle is tiny and increase sizably. We compare our results with the ones in the full Standard Model. Received: 24 October 1998 / Revised version: 16 February 1999 / Published online: 15 April 1999     

Renormalization group equations in local approximation

For a class of models with Ginzburg-Landau-Wilson functions of a local form it is proved that the spectrum of a renormalization group operator which is linearized near a fixed point is discrete, real, and limited from above. In the framework of a local model, critical exponents for the limitn= are calculated.     

Renormalization group equations of Briot-Bouquet type

The purpose of this paper is to investigate the renormalization group equations for massless models with two couplings and vanishing lowest order contribution of the β-function. It is shown that in this case the renormalization group equations can be reduced to others of Briot-Bouquet type. This observation permits to study in a simple and obvious manner the stability and asymptotic behaviour of solutions in the weak coupling limit.     

Renormalization group for matrix models with branching interactions

We develop a method to obtain the large-N renormalization group flows for matrix models of two-dimensional gravity plus branched polymers. This method gives precise results for the critical points and exponents for one-matrix models. We show that it can be generalized to two-matrix models and we recover the Ising critical points.     

Renormalization group equations and the gaussian spin model

Exact renormalization group equations are constructed for the one and two dimensional gaussian spin model by direct elimination of spins on a sublattice. They lead to the correct values of the critical exponents α, γ, ν and η.     

Renormalization group equations in lattice gauge theories

New recursion equations for renormalization group transformations of the Migdal-Kadanoff type are obtained for gauge systems including fermion variables on a d-dimensional Euclidean space-time lattice. It is shown that in the weak gauge coupling region these equations have β-functions similar to those of continuum field theories in the case of U(1), SU(2) gauge groups (QED, QCD). On the other hand in the strong-coupling limit there is an infrared attractive fixed point corresponding to a color-confining effective system in both groups. A possible entire trajectory of the non-Abelian system is briefly conjectured.     

Renormalization group equations for a two-dimensional nonlinear sigma-model with torsion

The renormalization group equations in the one-loop approximation are formulated for a two-dimensional nonlinear -model with torsion on a semisimple group manifold. Solutions of these equations are investigated for several particular cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 37–40, September, 1988.     

Renormalization-group analysis of the Kobayashi-Maskawa matrix

The one-loop renormalization-group equations for the quark mixing (Kobayashi-Maskawa) matrixV are derived, independent of one's weak interaction basis, in the standard model as well as in its two Higgs and supersymmetric extensions, and their numerical solutions are presented. While the mixing angles |V _ub |, |V _cb |, |V _td | and the phase-invariant measure of CP nonconservationJ all vary slowly with momentum, in the standard model they are predicted to increase in clear contrast to the two Higgs and supersymmetric extensions where they decrease with momentum.     

Renormalization group approach to matrix models via noncommutative space

Journal of High Energy Physics - We provide a detailed correspondence between G 4 gauge fluxes in F-theory compactifications with SU(n) and SU(n) × U(1) gauge symmetry and their Type IIB...     

Renormalization group equations for softly broken supersymmetry: The most general case

The renormalization group equations are derived for the most general gauge theory with softly broken supersymmetry. When specialized to the case that global supersymmetry breakdown is induced by spontaneously broken supergravity, the results exhibit new features which are important when applied to models which go beyond the simplest standard model with minimal particle content. As an application the renormalization group equations are given for a standard model with four Higgs doublets as well as for the minimal standard model including generation mixing, both in the framework of broken supergravity.     

A low temperature expansion for classicalN-vector models. II. Renormalization group equations

This paper continues the analysis of the low temperature expansions for classicalN-vector models started in [1]. A main part of it is a derivation of renormalization group equations and a construction of their solutions. To do this we have to introduce “a fluctuation integral” connected with a next renormalization transformation, and to make its preliminary analysis. The results of the paper are summarized in theorems stating that the renormalization transformation preserves the space of densitites, or actions described inductively in [1]. This work has been partially supported by the NSF Grant DMS-9102639.     

Renormalization group equations and the continuum limit of some renormalizable quantum field theories

The renormalization group equations for asymptotically and non-asymptotically free theories are discussed by exploiting the general properties of their integral curves. Some constraints are derived on the existence of a consistent continuum limit for pure Yang-Mills theories in an infinite quantization volume. An analogy between the far infrared behaviour of non-abelian gauge theories and the deep ultraviolet one of asymptotically free theories is discussed.