Gauge theory, holography & black holes Perspectives from string theory

This thesis is based on research performed in the context of string- and M-theory. It can be divided into two main parts: the first concerns a very effective organizing principle, also known as the worldvolume theory of multiple M5 branes, for the study of large classes of lower dimensional quantum field theories and myriad correspondences and dualities therein. Concretely, this organizing principle is put to use to explain a mysterious connection between correlation functions in specific two-dimensional conformal field theories and partition functions of four-dimensional supersymmetric Yang-Mills theories in the presence of a surface operator. The second part focuses on realizations of holography in string theory and further subdivides into two parts. It is the aim of the more progressive part to shed light on the holographic description of general spacetimes through use of the AdS/CFT correspondence. In particular, the microscopic, holographic descriptions of the de Sitter and Minkowski spacetimes are analyzed. The final, more traditional part is centered on a mathematical aspect of black hole microstate counting. The black holes considered live in five dimensions and have two independent angular momenta. Through the 4d/5d connection, they generalize the well-known quarter BPS dyons in four dimensions. The automorphic properties of a particular version of the counting function of these black holes are shown to enhance the known automorphic properties of the dyon counting function.