Studio dei Vuoti di Supergravità con tecniche numeriche

Since the discovery of supergravity, and its extended versions, it has always been interesting to investigate and analyze the structure of the scalar potential and its minima. There are several reasons for this study, spanning from phenomenology to cosmology, and more came out after the formulation of the AdS/CFT conjecture. Due to the great interest around this subject, many techniques have been developed along the years to compute and examine the vacua for those theories. Particular attention has been given from the scientific community to minima of the maximally supersimmetric supergravities, the rationale behind it being the fact that the field content and the lagrangian is completely specified by supersymmetry in these cases. This work moves in this frame and further develops the community’s endeavour aimed at better understanding the structures of supergravities and string theories and relating the latter to cosmological and phenomenological observations. In particular, maximally supersymmetric supergravities have been scrutinized in 5 and 7 spacetime dimensions, led by the idea of relating our results to conformal field theories in 4 and 6 dimensions respectively. In order to accomplish this highly complicated task, involving NP problems, several methods have been adopted throughout the work, in particular analytic techniques, first adopted in, allowed the scan of all the gaugings and of the whole space of theories in a simple way. We have deepened this analysis by employing algorithms used in the realm of post-quantum cryptography, succeeding therefore in pushing the analytical methods used for scrutinizing the vacua of supergravity theories further than what was previously possible. We went even further, and adopted a different perspective: instead of solving the system of quadratic equations, we tried a direct minimization of certain fitness functions related to the system of quadratic constraints. Implementing and developing numerical optimization algorithms used, nowadays, especially in the Artificial Intelligence universe, we have been able to analyze deeply the parameter space for maximal gauged supergravity theories. In certain special cases we also reconstructed or obtained the analytical solutions from the numerical results.