Color confinement and topology in lattice gauge theories

• Ano de defesa: 2025
• Autor(a) principal: Tonhon, Rafael Carlos Silva
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Center dominance; Center vortices; Confinamento; Confinement; Dominância de centro; Lattice gauge theory; Teoria de gauge na rede; Vórtices de centro
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/76/76134/tde-25032025-084717/

The lattice formulation of gauge theories provides a natural regularization procedure that allows us to study the infrared regime exactly, in a nonperturbative way, through Monte Carlo simulations. In this dissertation, in order to motivate the introduction of lattice discretization, we begin by formulating Quantum Mechanics in discrete space. Then, we develop the lattice formulation of Quantum Field Theory, studying the free scalar field and Yang-Mills theory. We show how the lattice works as a regularization scheme, which makes the field theory finite and well-defined. To recover the original theory, the continuum limit must be taken, which requires an analysis through the renormalization group. We discuss this for gauge theories. Then, we present the numerical methods used to generate configurations, and use them to study the center-dominance scenario for confinement, by measuring the static quark-antiquark potential and the gluon correlator. For this, we need to fix the Landau and the Maximal Center gauges via numerical techniques required for gauge fixing, which are also presented. In our own numerical simulations, we reproduce results indicating that the center vortices are the dominant degrees of freedom in the infrared regime, namely: 1) The linear behavior of the quark-antiquark potential can be reproduced by a vortex-only ensemble, while it disappears in a vortex-removed ensemble, 2) the removal of the vortices causes the gluon correlator to be suppressed in the infrared limit, which indicates that the long-range correlations are associated with these degrees of freedom.