Non-Renormalization Properties of the Chern-Simons Action Coupled to Matter

We analyze an abelian gauge model in 3 dimensions which includes massless scalar matter fields. By controlling the trace anomalies with a local dilatation Ward identity, we show that, in perturbation theory and within the BPHZL scheme, the Chern-Simons term has no radiative corrections. This implies, in particular, the vanishing of the corresponding $\beta$ function in the renormalization group equation.Comment: 11 page

Non-perturbative analysis of the Gribov-Zwanziger action

In the non-perturbative regime the usual gauge fixing is not sufficient due to the Gribov problem. To deal with it one can restrict the integration in the path integral to the first Gribov region by using the Gribov-Zwanziger action. In its local form it features additional auxiliary fields which mix with the gluon at the two-point level. We present an explicit infrared analysis of this action. We show that from the two possible scaling solutions obtained previously only one remains: It coincides exactly with the results from the Faddeev-Popov action, i.e., the ghost propagator is infrared enhanced and the gluon propagator infrared suppressed and the corresponding power law behavior is described by only one parameter kappa=0.5953. This corroborates the argument by Zwanziger that for functional equations it suffices to take into account the appropriate boundary conditions and no explicit restriction in the path integral measure is required.Comment: 3 pages, talk at the Quark Confinement and the Hadron Spectrum IX Conference, August 30 - September 3, 2010, Madri

Probing Mermin's inequalities violations through pseudospin operators

The violation of Mermin's inequalities is analyzed by making use of two different Bell setups built with pseudospin operators. Employing entangled states defined by means of squeezed and coherent states, the expectation value of Mermin's polynomials $M_n$ is evaluated for $n=3$ and $n=4$. In each case, we analyze the correlator $\langle M_n \rangle$ and identify the set of parameters leading to the violation of Mermin's inequalities and to the saturation of the bound predicted by Quantum Mechanics.Comment: 10 pages, 16 figure

BRST invariant formulation of the Bell-CHSH inequality in gauge field theories

A study of the Bell-CHSH inequality in gauge field theories is presented. By using the Kugo-Ojima analysis of the BRST charge cohomology in Fock space, the Bell-CHSH inequality is formulated in a manifestly BRST invariant way. The examples of the free four-dimensional Maxwell theory and the Abelian Higgs model are scrutinized. The inequality is probed by using BRST invariant squeezed states, allowing for large Bell-CHSH inequality violations, close to Tsirelson's bound. An illustrative comparison with the entangled state of two $1/2$ spin particles in Quantum Mechanics is provided.Comment: 12 pages. Revised version. Accepted for publication in SciPost Physic

A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories

The Gribov copies and their consequences on the infrared behavior of the gluon propagator are investigated in Euclidean Yang-Mills theories quantized in linear covariant gauges. Considering small values of the gauge parameter, it turns out that the transverse component of the gluon propagator is suppressed, while its longitudinal part is left unchanged. A Green function, G_{tr}, which displays infrared enhancement and which reduces to the ghost propagator in the Landau gauge is identified. The inclusion of the dimension two gluon condensate is also considered. In this case, the transverse component of the gluon propagator and the Green function G_{tr} remain suppressed and enhanced, respectively. Moreover, the longitudinal part of the gluon propagator becomes suppressed. A comparison with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations is provided.Comment: 20 page