About the Gribov problem in N=1 Super Yang-Mills

Full text: The BRST symmetry is a fundamental tool in order to prove the renormalizability of the theory, identify the physical subspace whose states have positive norm and guarantee that the restriction to the physical subspace of the scattering operator S is unitary. All this applies to the perturbative regime and to non-confining gauge theories for which the asymptotic fields and their corresponding elementary particles can be safely introduced. Things become much more complicated when the theory under investigation is a confining theory, such as Yang-Mills theories. Due to the nonperturbative phenomenon of color confinement, gluons are not part of the spectrum. In our case, the contact with the physical spectrum of the theory is encoded in the correlation functions of suitable composite colorless operators built out from the elementary gluon field. The Gribov-Zwanziger framework enables to take into account the nonperturbative effect of the Gribov copies by restricting the domain of integration in the functional integral to the first Gribov horizon. This restriction can be implemented within an Euclidean field theory framework. The corresponding action, known as the Gribov-Zwanziger action, enjoys the property of being local and renormalizable. As a consequence of the restriction of the domain of integration to the Gribov horizon, the gluon two-point correlation function gets deeply modified in the infrared region, displaying complex poles, so that it cannot describe a physical particle, being suitable for a confining phase. This work is a study of the N=1 four-dimensional super Yang-Mills theory in the light of the Gribov-Zwanziger framework, which enable to see, as already mentioned, the modified two-point correlation function of the gluon in the infrared region. But as we are studying a supersymmetric theory, this framework enable to study as well the modified two-point correlation function of the gluon super partner, the gluino. (author)