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

Poisson-Lie group of pseudodifferential symbols

We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of pseudodifferential symbols of an arbitrary real (or complex) order. We show that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP Poisson structures are naturally realized as restrictions of this Poisson structure to submanifolds of this ``universal'' Poisson--Lie group. Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebras in physical terminology) can be viewed as subspaces of the quotient (or Poisson reduction) of this Poisson--Lie group by the dressing action of the group of functions. Finally, we define an infinite set of functions in involution on the Poisson--Lie group that give the standard families of Hamiltonians when restricted to the submanifolds mentioned above. The Poisson structure and Hamiltonians on the whole group interpolate between the Poisson structures and Hamiltonians of Benney, KP and KdV flows. We also discuss the geometrical meaning of W_\infty as a limit of Poisson algebras W_\epsilon as \epsilon goes to 0.Comment: 64 pages, no figure

A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results

Recent lattice data have reported an infrared suppressed, positivity violating gluon propagator which is nonvanishing at zero momentum and a ghost propagator which is no longer enhanced. This paper discusses how to obtain analytical results which are in qualitative agreement with these lattice data within the Gribov-Zwanziger framework. This framework allows one to take into account effects related to the existence of gauge copies, by restricting the domain of integration in the path integral to the Gribov region. We elaborate to great extent on a previous short paper by presenting additional results, also confirmed by the numerical simulations. A detailed discussion on the soft breaking of the BRST symmetry arising in the Gribov-Zwanziger approach is provided.Comment: 38 pages, 9 figures, the content of section V has been extended and adapte

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

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

Fermi Surfaces of Diborides: MgB2 and ZrB2

We provide a comparison of accurate full potential band calculations of the Fermi surfaces areas and masses of MgB2 and ZrB2 with the de Haas-van Alphen date of Yelland et al. and Tanaka et al., respectively. The discrepancies in areas in MgB2 can be removed by a shift of sigma-bands downward with respect to pi-bands by 0.24 eV. Comparison of effective masses lead to orbit averaged electron-phonon coupling constants lambda(sigma)=1.3 (both orbits), lambda(pi)=0.5. The required band shifts, which we interpret as an exchange attraction for sigma states beyond local density band theory, reduces the number of holes from 0.15 to 0.11 holes per cell. This makes the occurrence of superconductivity in MgB2 a somewhat closer call than previously recognized, and increases the likelihood that additional holes can lead to an increased Tc.Comment: 7 pages including 4 figure

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

Infrared Features of the Landau Gauge QCD

The infrared features of Landau gauge QCD are studied by the lattice simulation of $\beta=6.0, 16^4, 24^4, 32^4$ and $\beta=6.4, 32^4, 48^4$. We adopt two definitions of the gauge field; 1) $U-$linear 2) $\log U$ and measured the gluon propagator and ghost propagator. Infrared singularity of the gluon propagator is less than that of tree level result but the gluon propagator at 0 momentum remains finite. The infrared singularity of ghost propagator is stronger than the tree level. The QCD running coupling measured by using the gluon propagator and the ghost propagator has a maximum $\alpha_s(p)\simeq 1$ at around $p=0.5GeV$ and decreases as $p$ approaches 0. The data are analyzed in use of formula of the principle of minimal sensitivity(PMS), the effective charge method and the contour-improved perturbation method, which suggest necessity of the resummation of perturbation series in the infrared region together with existence of the infrared fixed point. Kugo-Ojima parameter saturates at about -0.8 in contrast to the theoretically expected value -1.Comment: RevTex4, 9 pages, 10 eps figures, Typos corrected. To be published in Phys. Rev. D(2004

Landau gauge within the Gribov horizon

We consider a model which effectively restricts the functional integral of Yang--Mills theories to the fundamental modular region. Using algebraic arguments, we prove that this theory has the same divergences as ordinary Yang Mills theory in the Landau gauge and that it is unitary. The restriction of the functional integral is interpreted as a kind of spontaneous breakdown of the $BRS$ symmetry.Comment: 17 pages, NYU-TH-93/10/0