Computations on Field Theories with Super- and Higher Spin- Symmetry: Black Holes and Localization

In this thesis we study some aspects of field theories with super and higher spin symmetry. In the context of higher spin symmetry we restrict the study to 3 dimensions, we analyze the phase space of black hole solutions in the setting of $\mathfrak{sl}(3,\mathbb{R}) \oplus\mathfrak{sl}(3,\mathbb{R})$ Chern-Simons theory, to then move on to the $\infty$-dimensional algebra setting $\mathfrak{hs}(\l) \oplus\mathfrak{hs}(\l) $, where we construct black hole solutions and we couple these backgrounds to matter. \par We finish by introducing the idea of supersymmetric localization and we apply it to a four dimensional $\cn=2$ theories placed on a $SU(2)\times U(1)$ isometric $S^4$.