Abstract: This thesis is devoted to the study of the planar regime of N = 2 Lagrangian 4−dimensional superconformal field theories. In the first part of the thesis we study the matrix models that describe such theories upon performing supersymmetric localization on S^4. By studying the asymptotic expansion of the 1−loop partition function that defines the model, we find a unified description for a theory with classical gauge group G and conformal matter content. We develop novel combinatorial techniques to study these matrix models in the planar regime, these techniques allow us to obtain the full perturbative solution as a sum over a family of tree graphs that contain all the relevant contributions stemming from the connected correlators of the matrix model. For these theories we focus on the planar Free Energy and the supersymmetric Wilson loop of theories with a fraction of matter in the fundamental representation for which we are able to obtain the full perturbative series in the t'Hooft coupling. In the second part we focus our attention to the study of correlation functions of Chiral Primary Operators (CPO’s) in these theories, we generalize the matrix model techniques to a general class of models containing, possibly infinite, single and double trace terms and characterize their planar Free Energy and general correlation functions of matrix observables. We then proceed to unmix such correlators to study the extremal correlation functions of CPO’s and we find the exact solution or the 2− and 3−point functions in the planar limit. Finally, we study several Hermitian one-matrix models and certain examples of non-conformal field theories that also admit a matrix description. We obtain the exact solution for the planar Free Energy and we comment on the convergence of the perturbative expansion.

Tribunal members

President: Dr. Elli Pomoni
Secretary: Dr. Jorge Guillermo Russo
Vocal: Dr. Matteo Beccaria

Suplents:

Dr. Roberto Emparan
Dr. Carlos Núñez

Director: Dr. BARTOLOME SANTI FIOL NUNEZ

Tutor: Dr. JOAN SOTO RIERA