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

The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge

The local composite operator A^2 is added to the Zwanziger action, which implements the restriction to the Gribov region in Euclidean Yang-Mills theories in the Landau gauge. We prove the renormalizability of this action to all orders of perturbation theory. This allows to study the dimension two gluon condensate by the local composite operator formalism when the restriction is taken into account. The effective action is evaluated at one-loop order in the MSbar scheme. We obtain explicit values for the Gribov parameter and for the mass parameter due to , but the expansion parameter turns out to be rather large. Furthermore, an optimization of the perturbative expansion in order to reduce the dependence on the renormalization scheme is performed. The properties of the vacuum energy, with or without , are investigated. It is shown that in the original Gribov-Zwanziger formulation (without ), the vacuum energy is always positive at 1-loop order, independently from the renormalization scheme and scale. With , we are unable to come to a definite conclusion at the order considered. In the MSbar scheme, we still find a positive vacuum energy, again with a relatively large expansion parameter, but there are renormalization schemes in which the vacuum energy is negative, albeit the dependence on the scheme itself appears to be strong. We recover the well known consequences of the restriction, and this in the presence of : an infrared suppression of the gluon propagator and an enhancement of the ghost propagator. This behaviour is in qualitative agreement with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations.Comment: 42 pages, 10 .eps figures. v2: Version accepted for publication in Phys.Rev.D. Added references. Technical details have been collected in two appendice

A study of the gauge invariant, nonlocal mass operator Tr∫d4xFμν(D2)−1FμνTr \int d^4x F_{\mu\nu}(D^2)^{-1} F_{\mu\nu} in Yang-Mills theories

The nonlocal mass operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ is considered in Yang-Mills theories in Euclidean space-time. It is shown that the operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ can be cast in local form through the introduction of a set of additional fields. A local and polynomial action is thus identified. Its multiplicative renormalizability is proven by means of the algebraic renormalization in the class of linear covariant gauges. The anomalous dimensions of the fields and of the mass operator are computed at one loop order. A few remarks on the possible role of this operator for the issue of the gauge invariance of the dimension two condensates are outlined.Comment: 34 page

Post-Lie Algebras, Factorization Theorems and Isospectral-Flows

In these notes we review and further explore the Lie enveloping algebra of a post-Lie algebra. From a Hopf algebra point of view, one of the central results, which will be recalled in detail, is the existence of a second Hopf algebra structure. By comparing group-like elements in suitable completions of these two Hopf algebras, we derive a particular map which we dub post-Lie Magnus expansion. These results are then considered in the case of Semenov-Tian-Shansky's double Lie algebra, where a post-Lie algebra is defined in terms of solutions of modified classical Yang-Baxter equation. In this context, we prove a factorization theorem for group-like elements. An explicit exponential solution of the corresponding Lie bracket flow is presented, which is based on the aforementioned post-Lie Magnus expansion.Comment: 49 pages, no-figures, review articl

A study of the zero modes of the Faddeev-Popov operator in Euclidean Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions

Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2) Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4 dimensions.Comment: 18 pages. Text modifications. References added. Version accepted for publication in the EPJ

A2(2)A_{2}^{(2)} Gaudin model and its associated Knizhnik-Zamolodchikov equation

The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted $A_{2}^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$ independents Gaudin Hamiltonians. We also use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation solves the associated trigonometric system of Knizhnik-Zamolodchikov equations.Comment: 20 pages,no figure, typos corrected, LaTe

osp(1∣2)osp(1|2) off-shell Bethe ansatz equation with boundary terms

This work is concerned with the quasi-classical limit of the boundary quantum inverse scattering method for the $osp(1|2)$ vertex model with diagonal $K$-matrices. In this limit Gaudin's Hamiltonians with boundary terms are presented and diagonalized. Moreover, integral representations for correlation functions are realized to be solutions of the trigonometric Knizhnik-Zamoldchikov equations.Comment: 38 pages, minor revison, LaTe

Molecular Genetic Characterization of the Biosynthesis Cluster of a Prenylated Isoindolinone Alkaloid Aspernidine A in Aspergillus nidulans

Aspernidine A is a prenylated isoindolinone alkaloid isolated from the model fungus Aspergillus nidulans. A genome-wide kinase knock out library of A. nidulans was examined and it was found that a mitogen-activated protein kinase gene, mpkA, deletion strain produces aspernidine A. Targeted gene deletions were performed in the kinase deletion background to identify the gene cluster for aspernidine A biosynthesis. Intermediates were isolated from mutant strains which provided information about the aspernidine A biosynthesis pathway

Dynamical gluon mass generation from <A^2> in linear covariant gauges

We construct the multiplicatively renormalizable effective potential for the mass dimension two local composite operator A^2 in linear covariant gauges. We show that the formation of is energetically favoured and that the gluons acquire a dynamical mass due to this gluon condensate. We also discuss the gauge parameter independence of the resultant vacuum energy.Comment: 21 pages. 14 .eps figures. v2: minor modifications. v3: version accepted for publication in JHE