Quantum Chromodynamics (QCD) is believed to be the theory of strong interactions. At high energies, it has been successfully applied to explain the interactions in accelerators. At these energies, the method used to do the calculations is perturbation theory. But at low energies, since the strong coupling constant becomes large, perturbation theory is no longer applicable. Hence, one needs non-perturbative approaches. Some of these approaches are based on the fundamental QCD Lagrangian, such as the QCD sum rules or lattice calculations. Some others use an effective theory approach to relate experimental observables one to the other. Chiral Perturbation Theory (ChPT) is one of these approaches. In this thesis, we make a review of chiral perturbation theory and its applications to study the mixing phenomenon between the neutral pseudoscalar mesons eta and eta-prime.

In this thesis various holographic models are treated, which describe theories of fields where an internal symmetry is broken, either in relativistic contexts, or in case of violation of the Lorentz invariance.The first chapter opens with the revision of the notion of symmetry breaking in pure relativistic field theory. The case of spontaneous breaking and the Goldstone theorem are discussed, as well as the case of explicit breaking, where precise Ward identities between conserved current correlators and scalar operators loaded under such current are derived in a completely general way.We then consider two examples of non-relativistic field theories, which will be reproduced by holographic models: a model in which the invariance of boosts is broken by the presence of a chemical potential, and a model of Lifshitz's invariant theory. We show the non-relativistic realization of Ward's identities for the symmetry breaking.In the second chapter we briefly introduce the correspondence gravitation / gauge theory and we revise the central tool of this thesis, the holographic renormalization.In the third chapter, we show how to generate field theories with symmetry breaking by coupling a scalar field to a gauge field, and holographically deriving the Ward identities predicted by the field theory arguments, first in the Relativistic case. We also obtain an analytic expression for the scalar two-point function, where we know how to find the massless boson of Goldstone and the mass of linear mass in the explicit breaking parameter Of the Goldstone pseudo-boson, respectively in the purely spontaneous case and in the case of an explicit small break.We also consider the two-dimensional case on the edge, where we find that Coleman's theorem is eluded in the wide limit of $ N $, and Ward's identities are not affected.For non-relativistic cases, we first consider a non-abelian model in which the Lorentz invariance is broken: this situation makes it possible to observe so-called ~ B bosons which exhibit a quadratic dispersion relation and do not respect Not the law of a single Goldstone mode for each broken generator.Finally, we study in detail the holographic renormalization and the two-point functions for a conserved current and various scalar operators in a space-time of Lifshitz. We also find the Ward identities of symmetry breaking in their non-relativistic realization. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

The minimal renormalizable SO(10) Higgs model with the unified gauge sym- metry broken down by the adjoint representation 45S is known to suffer from tachyonic instabilities along all potentially realistic symmetry breaking chains. Few years ago, this issue has been identified as a mere relic of the tree-level cal- culations and the radiative corrections to the masses of the pair of the "most dangerous" pseudo-Goldstone scalars transforming as (8, 1, 0) and (1, 3, 0) with respect to the SU(3)c × SU(2)L × U(1)Y Standard model gauge group were com- puted. Remarkably enough, it turns out that in the minimal potentially realistic renormalizable realization of the model - consisting of 45S ⊕ 126S scalar and 45G gauge fields - there is third pseudo-Goldstone scalar, a full singlet with respect to the Standard model gauge group that, until recently, happened to escape the community's attention. In this thesis we computed the one-loop corrections to its mass employing two different methods within the effective potential approach. In both cases we reduced the complexity of our calculations by decomposition into the Standard model irreducible representations. In the end, we cross-checked the resulting formulae in four distinct symmetry breaking limits in which the pseudo- Goldstone mass was degenerated with those of...

Cette thèse porte sur l'étude de différents aspects de la physique nucléaire depuis les basses énergies jusqu'aux énergies intermédiaires. Pour les basses énergies, où la matière nucléaire est essentiellement constituée de nucléons en interaction, la partie I traite de la fusion-fission des noyaux super-lourds, et la partie II des règles de somme associées aux interactions de type Skyrme. Pour les énergies intermédiaires, la matière nucléaire étant alors considérée comme une phase hadronique principalement constituée de pions, la partie III se focalise sur l'hydrodynamique relativiste de la matière nucléaire avec brisure spontanée de symétrie chirale. Dans la partie I, on s'intéresse à la formation puis à la désexcitation des noyaux super-lourds. On étudie donc la formation du noyau composé avec effets de mémoire. Pour la désexcitation d'un noyau super-lourd, l'existence d'un puits isomérique dans la barrière de potentiel change la dynamique de désexcitation et augmente les temps de fission. Cette dernière étude pourrait être utile à l'étude de la dynamique de la fission des actinides. Dans la partie II, les règles de somme M1 et M3 associées aux potentiels phénoménologiques de type Skyrme sont calculées à partir de leurs définitions intrinsèques. On détermine alors M1 jusqu'au niveau tensoriel et M3 avec potentiel central. Dans la partie III, pour le traitement hydrodynamique de la matière hadronique appliqué aux collisions d'ions lourds on peut, en première approximation, écarter les modifications induites par la brisure spontanée de symétrie chirale mais pas celles dues à l'aspect dissipatif. / This study focuses on different aspects of nuclear physics from low energies to intermediate ones. For the low energies, the nuclear matter is essentially constituted from interacting nucleons. Part I is on the fusion-fission of super-heavy elements, while Part II is on the Skyrme interactions-associated sum rules. In the case of the intermediate energies, where the nuclear matter is considered as being an hadronic phase mainly constituted from pions, Part III is focused on nuclear matter relativistic hydrodynamics with spontaneous chiral symmetry breaking. In Part I, the formation and the desexcitation of super-heavy nuclei are being studied. We analyzed the formation of compound nuclei including the memory effects. For super-heavy nuclei desexcitation, the existence of isomeric state within the potential barrier modifies the desexcitation dynamics and increases the fission time. This latter study could be useful for the study of the actinides fission. In Part II, the phenomenological Skyrme effective interactions- associated M1 and M3 sum rules are being calculated based on their intrinsic definitions. We identify then M1 up to the tensorial level and M3 with central potential. In Part III, as for the hadronic matter hydrodynamics being applied to heavy ions collisions, and as a first approach only, we can neglect spontaneous chiral symmetry but certainly not the dissipative impact.