Study of the Gribov region in Euclidean Yang-Mills theories in the maximal Abelian gauge

Abstract

In this paper we address the issue of the Gribov copies in SU (N ), N > 2, Euclidean Yang-Mills theories quantized in the maximal Abelian gauge. A few properties of the Gribov region in this gauge are established. Similarly to the case of SU (2), the Gribov region turns out to be convex, bounded along the off-diagonals directions in field space, and unbounded along the diagonal ones. The implementation of the restriction to the Gribov region in the functional integral is discussed through the introduction of the horizon function, whose construction will be outlined in detail. The influence of this restriction on the behavior of the gluon and ghost propagators of the theory is also investigated together with a set of dimension two condensates. * malcapri@cbpf.br † ajgomez@uerj.br ‡

Gauge bosons at zero and finite temperature

“…The results here have concentrated on gauges fulfilling the perturbative Landau gauge condition. Therefore, many results in Coulomb gauge [18,85,467,468,, interpolating gauges [181,363,[501][502][503][504], linear covariant gauges [13,41,142,505,506], maximal Abelian gauges [158,505,[507][508][509][510][511][512][513][514], direct Laplacian gauges [56,[515][516][517], and other gauges [13,64,137,188,231,232,[518][519][520][521] have not been covered, though results at a similar level have been obtained in these cases as well. In particular, a similar situation with the finite-ghost case and scaling appears to be realized in Coulomb gauge [475,481,485,494], though this has to be investigated further.…”

Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

“…Although being out of the aim of the present work, it is worth mentioning that a treatment of the Gribov issue similar to that of the Landau gauge [3,16] can be implemented in the maximal Abelian gauge, see for instance refs. [6,7,8,9,10]. Let us turn thus to the characterization of the zero modes of the Faddeev-Popov operator M ab , which clearly affect expression (19).…”

“…On the other hand, the Hilbert norm A 2 is known to be deeply related to the Gribov issue. In fact, several properties of the Gribov region in both Landau and maximal Abelian gauge can be obtained by looking at all relative minima of A 2 along the gauge orbits, see [3,4,6,7,8,9,10].…”

A few remarks on the zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges

“…This has resulted in the so called Gribov-Zwanziger action [9,10] and its more recent refined version [11,12]. We underline that the functional f A [U ] can also be introduced in the maximal Abelian gauge, where a few properties of the corresponding Gribov region have been established [13].…”