Holography and holomorphy in quantum field theories and gravity

Resumen

This Ph.D. thesis deals with the application of complex analysis and holographic methods to study both the perturbative and the non-perturbative regimes of Quantum Field Theories and Gravity. Although Gravity does not admit a full quantum picture, its classical description is fine at tree level and it becomes useful for studying strongly coupled gauge theories through the gauge/gravity correspondence. We first study a generalization of the BCFW on-shell recursion relation, which allows us to characterize the tree-level scattering amplitudes of theories of massless particles in a fashion completely detached from the usual Feynman representation. This permits proposing a novel approach to the construction of theories which, despite being only valid at tree level and just for theories of massless particles, returns in a very simple manner some powerful facts, well-known from the traditional Lagrangian analysis. Then we focus on obtaining several new supergravity solutions dual to supersymmetric gauge theories with fundamental matter (flavor) in the Veneziano limit. These solutions must incorporate the backreaction of an infinite number of flavor branes. We choose to smear these branes in order to find analytical solutions. We find fully regular solutions describing the strongly coupled dynamics of flavor in the ABJM theory and in a SQCD-like theory. For the former, the solution has an AdS factor, and many checks can be done confirming that the supergravity solution is a faithful dual. For the latter, some checks can also be done, and more interestingly, phenomenological applications that might be relevant for Beyond-the-Standard-Model Physics can be found. Finally, we illustrate other uses of the gauge/gravity correspondence by finding supergravity solutions dual to theories exhibiting a Kutasov duality and SQCD-like theories in two and three dimensions.