Different viewpoints for the Gribov problem in Euclidean Yang-Mills Theories - Terin, Rodrigo Carmo (2020)
The infrared regime of Yang-Mills theories is still an unsolvable problem in theoretical physics. The attempt to describe in a clear and suitable way the phenomenon of confinement of gluons and quarks is far from being finished. In this manuscript, we study two different viewpoints for the quantization of Yang-Mills theories by taking into account the effects of Gribov copies. The first one is the well-known Gribov-Zwanziger framework reinvented by including bosonic and fermionic gauge-invariant local composite fields through a detailed construction of a nonperturbative BRST symmetry. This gives us the possibility to extend this model to another class of gauges in a correct manner, the so-called linear covariant gauges. Then, we prove its renormalizability to all orders in a loop expansion by using the algebraic renormalization method. The Other one is the Serreau-Tissier approach, in this framework we establish a good explanation for the generation of the gauge field (gluon) mass added in the particular Curci-Ferrari phenomenological model proposed by M. Tissier and N. Wschebor by using the symmetry restoration phenomenon. To accomplish that, we also discuss the similarities between the nonlinear sigma models in two space-time dimensions and quantum chromodynamics.