Study of the all orders multiplicative renormalizability of a local matter confining Gribov-Zwanziger action in the MAG

Abstract

We address the issue of the all order multiplicative renormalizability of $SU(2)$ Gribov-Zwanziger theories quantized in the maximal Abelian gauge in presence of confined matter fields. The non-linear character of the maximal Abelian gauge requires the introduction of quartic interaction terms in the Faddeev-Popov ghosts as well as in the localizing Zwanziger fields, extended a well known feature of this gauge. We show that, when scalar matter fields are introduced, a second quartic interaction term between scalar fields, Faddeev-Popov ghosts and Zwanziger-like fields naturally arises. A BRST invariant action accounting for those quartic interaction terms is identified and proven to be multiplicative renormalizable to all orders by means of the algebraic renormalization procedure.

28 pages. Some expressions and typos were corrected, discussions added, arXiv admin note: text overlap with arXiv:1502.00562