An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions

The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev-Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU(N) Yang-Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribov's no-pole condition, can be implemented by demanding a nonvanishing expectation value for a functional of the gauge fields that turns out to be Zwanziger's horizon function. The action allowing to implement this condition is the Gribov-Zwanziger action. This establishes in a precise way the equivalence between Gribov's no-pole condition and Zwanziger's horizon condition.Comment: 11 pages, typos corrected, version accepted for publication in Phys. Lett.

A study of the Higgs and confining phases in Euclidean SU(2) Yang-Mills theories in 3d by taking into account the Gribov horizon

We study SU(2) three-dimensional Yang-Mills theories in presence of Higgs fields in the light of the Gribov phenomenon. By restricting the domain of integration in the functional integral to the first Gribov horizon, we are able to discuss a kind of transition between the Higgs and the confining phase in a semi-classical approximation. Both adjoint and fundamental representation for the Higgs field are considered, leading to a different phase structure.Comment: 12 pages. Version accepted for publication in the EPJ

The universal character of Zwanziger's horizon function in Euclidean Yang-Mills theories

In light of the recently established BRST invariant formulation of the Gribov-Zwanziger theory, we show that Zwanziger's horizon function displays a universal character. More precisely, the correlation functions of local BRST invariant operators evaluated with the Yang-Mills action supplemented with a BRST invariant version of the Zwanziger's horizon function and quantized in an arbitrary class of covariant, color invariant and renormalizable gauges which reduce to the Landau gauge when all gauge parameters are set to zero, have a unique, gauge parameters independent result, corresponding to that of the Landau gauge when the restriction to the Gribov region $\Omega$ in the latter gauge is imposed. As such, thanks to the BRST invariance, the cut-off at the Gribov region $\Omega$ acquires a gauge independent meaning in the class of the physical correlators.Comment: 14 pages. v2: version accepted by Phys.Lett.

Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge

The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. The non-renormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N=1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three loop calculation.Comment: 15 pages, minor text improvements, references added. Version accepted for publication in the EPJ

Experimental determination of the non-extensive entropic parameter qq

We show how to extract the $q$ parameter from experimental data, considering an inhomogeneous magnetic system composed by many Maxwell-Boltzmann homogeneous parts, which after integration over the whole system recover the Tsallis non-extensivity. Analyzing the cluster distribution of La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ manganite, obtained through scanning tunnelling spectroscopy, we measure the $q$ parameter and predict the bulk magnetization with good accuracy. The connection between the Griffiths phase and non-extensivity is also considered. We conclude that the entropic parameter embodies information about the dynamics, the key role to describe complex systems.Comment: Submitted to Phys. Rev. Let