Scattering Amplitudes in Confining Theories and Holography

Resumo

The AdS/CFT correspondence or holographic duality allows us to describe physical systems in strongly coupled regimes where the traditional tools at our disposal such as perturbative analysis cannot be applied. This thesis is focused on the development of a method to compute scattering amplitudes in theories confining with holographic duals using the AdS/CFT correspondence. These confining theories present a "mass gap" and a discrete mass spectrum. A method has been developed to calculate scattering amplitudes and scattering lengths in elastic scattering processes using holographic duality. These quantities capture the basic characteristics of the interaction in the dispersion process, i.e. whether the interaction is attractive or repulsive. This method consists of identifying the residues of Green's functions in dual gravitational theory with the amplitudes in field theory. This procedure was applied to already known systems. These holographic models, obtained from string theory, are dual to confining field theories and present different geometric realizations. Applying our method, we have obtained in the first case the relationship between the scattering length and the mass of the particles participating in the interaction, as well as the relationship between the scattering length and the conformal dimension of the operators that create these particles and their mass spectrum. Finally, we have obtained the value of the coefficients of the chiral lagrangian as well as the value of the pion decay constant by applying our method to a model that includes these particles and presents the symmetries of the chiral theory. The thesis contains seven chapters. The first chapter consists of an introduction where the context of this work is exposed. Chapter 2 reviews several topics related to quantum field theory necessary for the thesis. Chapter 3 presents the holographic duality and its main characteristics. Chapter 4 presents and develops a method for calculating the scattering amplitude and the scattering length within the framework of AdS/CFT correspondence. In Chapter 5 this method is applied to three different models to obtain the scattering length and mass spectrum. In Chapter 6 this method is applied to the process of dispersion of pions to obtain its scattering amplitude. Finally, the conclusions are given in Chapter 7