000101129 001__ 101129 000101129 005__ 20210520140815.0 000101129 037__ $$aTESIS-2021-116 000101129 041__ $$aeng 000101129 080__ $$a53 000101129 1001_ $$aRoyo Amondarain, Eduardo 000101129 24500 $$aNon-perturbative physics in lattice gauge theories 000101129 260__ $$aZaragoza$$bUniversidad de Zaragoza, Prensas de la Universidad$$c2021 000101129 300__ $$a132 000101129 4900_ $$aTesis de la Universidad de Zaragoza$$v2021-116$$x2254-7606 000101129 500__ $$aPresentado: 28 01 2021 000101129 502__ $$aTesis-Univ. Zaragoza, , 2021$$bZaragoza, Universidad de Zaragoza$$c2021 000101129 506__ $$aby$$bCreative Commons$$c3.0$$uhttp://creativecommons.org/licenses/by/3.0/es 000101129 520__ $$aA few decades have passed since quantum chromodynamics (QCD) was established <br />as the theory describing strong interactions. It is broadly accepted as one of <br />the most successful theories in modern physics, and it has been extensively <br />tested, both from the theoretical and the experimental perspectives.<br />At high energies, QCD is asymptotically free, which means that its <br />fundamental constituents, quarks and gluons, interact with a strength that <br />decreases as the energy scale reaches higher values. In this regime, it is <br />feasible to use perturbation theory to resolve short distance interactions. <br />On the other hand, for not-so-high energies, the strong interaction cannot <br />be reduced to a converging series of Feynman diagrams. In fact, one of the <br />characteristic properties of QCD is the so-called color-confinement. In this <br />purely non-perturbative regime, there are few techniques that can analyze the <br />theory successfully. Probably the most well-established of them is lattice <br />QCD. Since the foundational work of Wilson in 1974, the success of the lattice <br />approach has been growing consistently over time. Many milestones <br />have already been reached, including precise simulations that account for the <br />effects of virtual quark loops, the determination of the light hadron spectrum <br />with fully controlled systematics or, more recently, the computation of the <br />isospin splittings with great agreement with the experimental data.<br />For the above reasons, QCD is believed to be the correct theory describing <br />strong interactions, both for high and low energies, and lattice QCD is <br />recognized by the community as a trustworthy ab initio approach that <br />has an useful interaction with experiment, paraphrasing Wilson. However, <br />there are some fundamental topics that still constitute open questions. <br />At least two problems share this status: the behavior of matter at finite <br />baryonic density and the studies involving topological effects in QCD. The <br />main difficulty behind the modest progress achieved in both areas is the same: <br />the action of the theory is complex, and there is no known reformulation that can <br />avoid the appearance of a severe sign problem (SSP).<br />In this context, the main part of this thesis has been devoted to study models <br />which suffer from a SSP, such as the two-dimensional Ising model within an <br />imaginary magnetic field or the massive 1-flavor Schwinger model with a theta <br />term. In the first case, we study the well-known model by means of analytical <br />techniques, exploring a region of the parameter space somewhat unattended by <br />the literature, possibly due to the difficulty of applying either analytical <br />or numerical techniques. Secondly, and with the aim of engaging with QCD-like <br />systems with a theta term and to develop further the methods dealing with the <br />SSP, we have studied the massive 1-flavor Schwinger model with a $\theta$ term, <br />which corresponds to QED in $1+1$ dimensions, and is in fact broadly used as its <br />toy model. Moreover, defining the topological charge on the lattice is almost <br />trivial in this model, in contrast with any of the usual definitions of this <br />observable in lattice QCD, which are much more involved. As a byproduct of this <br />line of work, and driven by the necessity of optimizing further our previous <br />algorithms, we have also analysed the 2-flavor version of the Schwinger model. <br />In this case, we have bypassed the computation of the full fermionic determinant <br />by following an approach based on the use of pseudofermions.<br />Finally, beyond the study of systems afflicted by a SSP, another topic within <br />lattice QCD has been treated during the development of this thesis: the strong <br />running coupling alpha_S. Its dependence with the momentum transfer, which <br />encodes the underlying interactions of quarks and gluons in the QCD framework, <br />constitutes a very active field of research, that includes a large variety of <br />approaches. At large momenta, where perturbative QCD can be applied, both <br />experimental and theoretical methods try to provide the most accurate <br />approximation. In this context, lattice-based strategies have been capable of <br />delivering results both in the infrared region and in the high energy regime, <br />where in fact they provide the most precise determination of the coupling <br />constant. Our work can be framed precisely into these approaches that come <br />from lattice QCD, and it relies upon a ghost-gluon vertex computation.<br /> 000101129 520__ $$a<br /> 000101129 521__ $$97076$$aPrograma de Doctorado en Física 000101129 6531_ $$afisica teorica 000101129 6531_ $$afisica teorica de altas energias 000101129 6531_ $$ateoria cuantica de campos 000101129 700__ $$aAzcoiti Pérez, Vicente $$edir. 000101129 700__ $$aFollana Adín, Eduardo $$edir. 000101129 7102_ $$aUniversidad de Zaragoza$$b 000101129 830__ $$9488 000101129 8560_ $$ftdr@unizar.es 000101129 8564_ $$s1614831$$uhttps://zaguan.unizar.es/record/101129/files/TESIS-2021-116.pdf$$zTexto completo (eng) 000101129 909CO $$ooai:zaguan.unizar.es:101129$$pdriver 000101129 909co $$ptesis 000101129 9102_ $$a$$b 000101129 980__ $$aTESIS