Renormalization Group and Conformal Symmetry Breaking in the Chern-Simons Theory Coupled to Matter

The three-dimensional Abelian Chern-Simons theory coupled to a scalar and a fermionic field of arbitrary charge is considered in order to study conformal symmetry breakdown and the effective potential stability. We present an improved effective potential computation based on two-loop calculations and the renormalization group equation: the later allows us to sum up series of terms in the effective potential where the power of the logarithms are one, two and three units smaller than the total power of coupling constants (i.e., leading, next-to-leading and next-to-next-to-leading logarithms). For the sake of this calculation we determined the beta function of the fermion-fermion-scalar-scalar interaction and the anomalous dimension of the scalar field. We shown that the improved effective potential provides a much more precise determination of the properties of the theory in the broken phase, compared to the standard effective potential obtained directly from the loop calculations. This happens because the region of the parameter space where dynamical symmetry breaking occurs is drastically reduced by the improvement discussed here.Comment: 29 pages, 10 figures, 1 tabl

Closing the SU(3)L⊗U(1)XSU(3)_L\otimes U(1)_X Symmetry at Electroweak Scale

We show that some models with $SU(3)_C\otimes SU(3)_L\otimes U(1)_X$ gauge symmetry can be realized at the electroweak scale and that this is a consequence of an approximate global $SU(2)_{L+R}$ symmetry. This symmetry implies a condition among the vacuum expectation value of one of the neutral Higgs scalars, the $U(1)_X$'s coupling constant, $g_X$, the sine of the weak mixing angle $\sin\theta_W$, and the mass of the $W$ boson, $M_W$. In the limit in which this symmetry is valid it avoids the tree level mixing of the $Z$ boson of the Standard Model with the extra $Z^\prime$ boson. We have verified that the oblique $T$ parameter is within the allowed range indicating that the radiative corrections that induce such a mixing at the 1-loop level are small. We also show that a $SU(3)_{L+R}$ custodial symmetry implies that in some of the models we have to include sterile (singlets of the 3-3-1 symmetry) right-handed neutrinos with Majorana masses, being the see-saw mechanism mandatory to obtain light active neutrinos. Moreover, the approximate $SU(2)_{L+R}\subset SU(3)_{L+R}$ symmetry implies that the extra non-standard particles of these 3-3-1 models can be considerably lighter than it had been thought before so that new physics can be really just around the corner.Comment: 32 pages, no figure, RevTeX. Some typos correcte

Scaling limit for a drainage network model

We consider the two dimensional version of a drainage network model introduced by Gangopadhyay, Roy and Sarkar, and show that the appropriately rescaled family of its paths converges in distribution to the Brownian web. We do so by verifying the convergence criteria proposed by Fontes, Isopi, Newman and Ravishankar.Comment: 15 page

Non-perturbative fixed points and renormalization group improved effective potential

The stability conditions of a renormalization group improved effective potential have been discussed in the case of scalar QED and QCD with a colorless scalar. We calculate the same potential in these models assuming the existence of non-perturbative fixed points associated to a conformal phase. In the case of scalar QED the barrier of instability found previously is barely displaced as we approach the fixed point, and in the case of QCD with a colorless scalar not only the barrier is changed but the local minimum of the potential is also changed.Comment: 6 pages, 8 figures, References added. Matching the journal versio

The use of circular economy practices in SMEs across the EU

This study explores the circular economy (CE) practices of Small and Medium Enterprises (SMEs) in the 28 European Union (EU) member states. Five measures of CE are studied, namely Re-planning the way water is used to minimize usage and maximize re-usage, Using renewable energy, Re-planning energy usage to minimize consumption, Minimizing waste by recycling or reusing waste or selling it to another firm, and Redesigning products and services to minimize the use of materials or using recycled materials. Multilevel ordinal probit models that control within- and between-variability across European Union countries are estimated. Results show that CE measures across EU countries are very heterogeneous. At the firm level, we find that firm size (number of employees and total turnover in 2015) and percentage of firms’ turnover invested in R&D in 2015 are significant in explaining within-country variations. The multilevel structure (between-country variability) accounts for 6.1%–15.1% of the total variability of CE measures. These results have implications for the design of framework policies at EU level given that the firms surveyed are SMEs, the segment in which these CE measures most need improved planning and implementation.info:eu-repo/semantics/acceptedVersio

Generation of higher derivatives operators and electromagnetic wave propagation in a Lorentz-violation scenario

We study the perturbative generation of higher-derivative operators as corrections to the photon effective action, which are originated from a Lorentz violation background. Such corrections are obtained, at one-loop order, through the proper-time method, using the zeta function regularization. We focus over the lowest order corrections and investigate their influence in the propagation of electromagnetic waves through the vacuum, in the presence of a strong, constant magnetic field. This is a setting of experimental relevance, since it bases active efforts to measure non linear electromagnetic effects. After surprising cancellations of Lorentz violating corrections to the Maxwell's equation, we show that no effects of the kind of Lorentz violation we consider can be detected in such a context.Comment: v2: 13 pages, no figures, section IV considerably rewritten, main results unchanged and are now obtained in a simpler way. To appear in PL