• Holography
• interaction
• deuteron
• baryons
• Sakai-Sugimoto

In this thesis we build a model that can be used to describe baryon dynamics, and in particular we look for an interaction potential between the basic nucleons (proton and neutron). To do that, we follow an approach that mixes two ideas: the description of particles as topological solitons in nonlinear field theory and the Anti de Sitter / Conformal Field Theory (AdS/CFT) correspondence.

We study large N QCD by studying the action of the low energy modes of a string theory. We see that this theory adimts topological solitons called instantons, and quantization of the degrees of freedom of an instantonic field of charge one creates a quantum system with states whose transformation properties and quantum numbers are just right to interpret them as states with a definite rest energy, an impulse, a spin and an isospin degrees of freedom. In this picture, we build a charge two field configuration by gluing together two single charge instanton solutions. Due to the non linearity of the theory, this solution is approximative, and we show that it holds in the limit of large 't Hooft coupling. In those limits, we compute the energy of this field configuration, and interpret the result as a potential of interaction between instantons. This is proposed as a classical potential for baryon interaction, and its structure as infinite sum of Yukawa monopole and dipole interactions is interpreted as the classical analogue of an exchange interaction with a meson mediator. We show how the masses of baryons and mesons can be computed in this model.

After computing the potential, we quantize the coordinates of the two instanton fields, and impose physical constraints to restrict the spectrum of the system. We see that the internal degrees of freedom of the system can be rearranged and interpreted as total spin and isospin of the system, and that they assume only integer values. Among the states that are compatible with our constraints, we find a state with the right angular quantum numbers (spin one and isospin zero) and interpret it as deuteron state. We compute the stability of this state with respect to the splitting in two separated baryons, and make a similar analysis for other low energy states in the spectrum. We comment the large N and large 't Hooft coupling limit, comparing our results with the qualitative predictions of large N QCD, and extrapolate the binding energy of the deuteron.