Study of the all orders multiplicative renormalizability of a local confining quark action in the Landau gauge

The inverse of the Faddeev–Popov operator plays a pivotal role within the Gribov–Zwanziger approach to the quantization of Euclidean Yang–Mills theories in Landau gauge. Following a recent proposal (Capri et al., 2014), we show that the inverse of the Faddeev–Popov operator can be consistently coupled to quark fields. Such a coupling gives rise to a local action while reproducing the behaviour of the quark propagator observed in lattice numerical simulations in the non-perturbative infrared region. By using the algebraic renormalization framework, we prove that the aforementioned local action is multiplicatively renormalizable to all orders.