DUALITIES IN FOUR, THREE AND TWO DIMENSIONS

Modern Physics is grounded on two apparently irreconcilable descriptions: Quantum Field Theories (QFTs) and Gravity. Two major challenges for Theoretical Physics are represented by the understanding of the strong coupling regime of Quantum Field Theory and by the reconciling of QFT with classical gravity via a quantum theory of gravity. In this setting, the concept of duality plays a prominent role. Among the most remarkable results in supersymmetric field theories are infrared dualities, where two distinct UV theories share an equivalent IR description in terms of different degrees of freedom. The usefulness of such dualities lies in the fact that they usually provide a weakly-coupled description of the strong coupling regime. At the same time, the AdS/CFT correspondence represents a cornerstone of modern physics, as it offers a concrete and mathematically robust framework in which quantum gravity emerges from a well-defined dual description in terms of a quantum field theory. The present Thesis explores recent results regarding the role of dualities in Theoretical Physics. The Thesis is divided into four parts. The first three parts are devoted to the study of infrared dualities in four, three and two dimensions respectively. A central topic explored is the idea of dimensional reduction, which allows for connecting different dualities across dimensions, providing in this way a common origin to many seemingly unrelated dualities. Additionally, supersymmetric partition functions provide a crucial tool to discover and check new claimed dualities. In the first part we derive a new web of dualities obtained by considering baryonic dangerously irrelevant deformations, connecting SU(N) and USp(2N) gauge theories. In the second part we discuss a double-scaling approach to the 3d reduction of 4d dualities. Subsequently, we study the dimensional reduction of the 4d web described in the previous part to uncover new dualities in 3d connecting SU(N), USp(2N) and SO(N) gauge theories. In the third part we explore new classes of 2d N=(0,2) dualities involving antisymmetric matter and discuss their four dimensional origin via dimensional reduction. Finally, the last part is centered around the study of Black Hole entropy in field theory within the AdS/CFT correspondence. We analyze the role of insertion of Gukov-Witten surface defects as order parameters for the Hawking-Page phase transition in gravity, and study S-duality in field theory via the AdS/CFT correspondence.