Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGauge copies and the fate of background independence in Yang-Mills theories: a leading order analysis
145
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this work we investigate the effects of the Gribov prescription to get rid of zero-modes of the Faddeev-Popov operator, at one-loop order in perturbation theory, in the Landau-DeWitt gauge. Quantum fluctuations are taken around a transverse background gauge field. The one-loop effective action is explicitly computed, and the behavior of the gauge and ghost fields propagators are carefully investigated. At one-loop and for generic transverse background configurations the effective action is found to be textit{not} background invariant, as expected, due to a non-vanishing background contribution. The gauge field propagator has the same form as in the case {where the} background is a trivial field, $i.e.$ with complex conjugate poles, which are modified by the corresponding gap equation. The ghost-anti-ghost propagator still displays its enhanced $sim p^{-4}$ behavior.
rate research
Read More
We study the Gribov problem in four-dimensional topological Yang-Mills theories following the Baulieu-Singer approach in the (anti-)self-dual Landau gauges. This is a gauge-fixed approach that allows to recover the topological spectrum, as first constructed by Witten, by means of an equivariant (or constrained) BRST cohomology. As standard gauge-fixed Yang-Mills theories suffer from the gauge copy (Gribov) ambiguity, one might wonder if and how this has repercussions for this analysis. The resolution of the small (infinitesimal) gauge copies, in general, affects the dynamics of the underlying theory. In particular, treating the Gribov problem for the standard Landau gauge condition in non-topological Yang-Mills theories strongly affects the dynamics of the theory in the infrared. In the current paper, although the theory is investigated with the same gauge condition, the effects of the copies turn out to be completely different. In other words: in both cases, the copies are there, but the effects are very different. As suggested by the tree-level exactness of the topological model in this gauge choice, the Gribov copies are shown to be inoffensive at the quantum level. To be more precise, following Gribov, we discuss the path integral restriction to the Gribov horizon. The associated gap equation, which fixes the so-called Gribov parameter, is however shown to only possess a trivial solution, making the restriction obsolete. We relate this to the absence of radiative corrections in both gauge and ghost sectors. We give further evidence by employing the renormalization group which shows that, for this kind of topological model, the gap equation indeed forbids the introduction of a massive Gribov parameter.
Various gauge invariant but non-Yang-Mills dynamical models are discussed: Precis of Chern-Simons theory in (2+1)-dimensions and reduction to (1+1)-dimensional B-F theories; gauge theories for (1+1)-dimensional gravity-matter interactions; parity and gauge invariant mass term in (2+1)-dimensions.
Recently, based on a new procedure to quantize the theory in the continuum, it was argued that Singers theorem points towards the existence of a Yang-Mills ensemble. In the new approach, the gauge fields are mapped into an auxiliary field space used to separately fix the gauge on different sectors labeled by center vortices. In this work, we study this procedure in more detail. We provide examples of configurations belonging to sectors labeled by center vortices and discuss the existence of nonabelian degrees of freedom. Then, we discuss the importance of the mapping injectivity, and show that this property holds infinitesimally for typical configurations of the vortex-free sector and for the simplest example in the one-vortex sector. Finally, we show that these configurations are free from Gribov copies.
The background gauge renormalization of the first order formulation of the Yang-Mills theory is studied by using the BRST identities. Together with the background symmetry, these identities allow for an iterative proof of renormalizability to all orders in perturbation theory. However, due to the fact that certain improper diagrams which violate the BRST symmetry should be removed, the renormalizability must be deduced indirectly. The recursive method involves rescalings and mixings of the fields, which lead to a renormalized effective action for the background field theory.
Using the background field method, we study in a general covariant gauge the renormalization of the 6-dimensional Yang-Mills theory. This requires background gauge invariant counterterms, some of which do not vanish on shell. Such counterterms occur, even off-shell, with gauge-independent coefficients. The analysis is done at one loop order and the extension to higher orders is discussed by means of the BRST identities. We examine the behaviour of the beta function, which implies that this theory is not asymptotically free.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
