545 research outputs found
Infrared scaling solutions beyond the Landau gauge: The maximally Abelian gauge and Abelian infrared dominance
Functional equations like exact renormalization group and Dyson-Schwinger
equations have contributed to a better understanding of non-perturbative
phenomena in quantum field theories in terms of the underlying Green functions.
In Yang-Mills theory especially the Landau gauge has been used, as it is the
most accessible gauge for these methods. The growing understanding obtained in
this gauge allows to proceed to other gauges in order to obtain more
information about the relation of different realizations of the confinement
mechanism. In the maximally Abelian gauge first results are very encouraging as
a variant of Abelian infrared dominance is found: The Abelian part of the gauge
field propagator is enhanced at low momenta and thereby dominates the dynamics
in the infrared. Its role is therefore similar to that of the ghost propagator
in the Landau gauge, where one denotes the corresponding phenomenon as ghost
dominance. Also the ambiguity of two different types of solutions (decoupling
and scaling) exists in both gauges. Here we present how the two solutions are
related in the maximally Abelian gauge. The intricacy of the system of
functional equations in this gauge required the development of some new tools
and methods as, for example, the automated derivation of the equations by the
program DoFun. We also present results for linear covariant and ghost
anti-ghost symmetric gauges.Comment: 10 pages, 2 figures, Proceedings of The Many faces of QCD, Nov. 1-5
2010, Ghent, Belgiu
On the Analytic Structure of Scalar Glueball Operators
The correlator of the square of the Yang-Mills field-strength tensor
corresponds to a scalar glueball, i.e., to a bound-state formed by gluonic
ingredients only. It has quantum numbers 0++ and its mass, as predicted by
different theoretical approaches, is expected to lie between 1 and 2 GeV. Here
we restrict our considerations to the Born level, that is, we consider the
correlator to zeroth order in the coupling. Gluonic self-interaction is taken
into account indirectly by using non-perturbative gluon propagators. The
employed closed expressions are motivated by lattice and Dyson-Schwinger
studies. The analytic continuation of the integrals themselves is complicated
by additional obstructive structures like branch cuts and poles that are
induced by the inner integral in the complex plane of the outer integration
variable. We deal with this problem by deforming the outer integration contour
accordingly. For different input gluon propagators we find a positive glueball
spectral density which is required for physical states. Poles are, however,
absent which is most likely an artifact of working at Born level.Comment: 8 pages, 5 figure
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
Three-point vertex functions in Yang-Mills Theory and QCD in Landau gauge
Solutions for the three-gluon and quark-gluon vertices from Dyson-Schwinger
equations and the three-particle irreducible formalism are discussed. Dynamical
quarks (``unquenching'') change the three-gluon vertex via the quark-triangle
diagrams which themselves include fully dressed quark-gluon vertex functions.
On the other hand, the quark-swordfish diagram is, at least with the model used
for the two-quark-two-gluon vertex employed here, of minor importance. For the
leading tensor structure of the three-gluon vertex the "unquenching" effect can
be summarized for the nonperturbative part as a shift of the related dressing
function towards the infrared.Comment: Talk given by Adrian L. Blum at XIIth Quark Confinement and the
Hadron Spectrum, August 28 - September 04, 2016, Thessaloniki, Greec
Lower dimensional Yang-Mills theory as a laboratory to study the infrared regime
Lattice studies of the infrared regime of gauge theories are complicated by
the required extensive limits, the performed gauge fixing and the demand for
high statistics. Using a general power counting scheme for the infrared limit
of Landau gauge SU(N) Yang-Mills theory in arbitrary dimensions we show that
the infrared behavior of Greens functions is both qualitatively and
quantitatively similar in two, three and four spacetime dimensions. Therefore,
lower dimensional lattice simulations can serve as a simplified laboratory to
analyze the presently applied approximations and to obtain first results for
higher correlation functions.Comment: 7 pages, 6 figures; talk presented at Lattice 200
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