Aspects of the Gribov problem in Euclidean Yang-Mills theories

TL;DR

This thesis investigates the Gribov problem in Euclidean Yang-Mills theories with matter, proposing that gauge sector effects at low energies influence matter fields through an effective non-local mass term, revealing non-perturbative phenomena.

Contribution

It introduces the idea that the Gribov horizon impacts matter fields via a dynamically generated non-local mass term, linking gauge and matter sectors in the infrared regime.

Findings

Evidence of interplay between gauge and matter sectors at low energies

Proposal of a non-local mass term for matter fields influenced by the Gribov horizon

Non-perturbative effects in matter fields related to the gauge sector

Abstract

The content of the present thesis is based on the papers [arXiv:1510.07886 [hep-th]][arXiv:1505.02287 [hep-th]][arXiv:1401.6303 [hep-th]][arXiv:1309.1402 [hep-th]][arXiv:1305.4155 [hep-th]][arXiv:1212.1003 [hep-th]][arXiv:1210.4734 [hep-th]] and is devoted to the study of aspects of the Gribov problem in Euclidean Yang-Mills theories coupled to matter fields. Here, we present some, mathematical and physical, evidences that point to the existence of a possible interplay between the gauge sector and the matter sector, in regimes of sufficiently ow energy (known as the infrared regime). In other words, we claim that an effect in the vector boson sector of Nature due to strong interactions (the Standard Model), at low energies, may be reflected in the matter sector, in the same regime. Specifically, we propose that the Gribov horizon function of the gauge sector may be felt by the matter field, and that it would be described by an effective non-local mass term attached to the matter field. Such a term seems to be dynamically generated and accounts for non-perturbative aspects of the matter field.