Generalized Symmetries in Supergravities and Superconformal Field Theories via String Theory

Abstract

In this dissertation, we study the generalized symmetries in supergravities and superconformal field theories from the string theory perspective. Part one is devoted to the study of string universality in high spacetime dimensions. Answering this question requires us to combine the following two approaches. In the "top-down" approach, We focus on supergravity theories in 7, 8, and 9 dimensional spacetime with 16 supercharges. We emphasize two discrete aspects of these theories: generalized global symmetries and frozen singularities. We give an exhaustive classification of IIB supergravity theory in 8D, particularly emphasizing these two discrete aspects. In the "bottom-up" approach, we present a consistency condition of general 8D supergravity theories involving their higher-form symmetries use it to rule out many global structures of the gauge groups in 8D supergravity theories that do not admit string theory constructions. Part two studies the generalized global symmetries of geometrically-engineered quantum field theories via string theory. We examined branes wrapping on relative topological cycles that give heavy defects that are charged under generalized global symmetries, which can then be used to construct new lower-dimensional theories. By investigating the string theory origin of the topological operators, we provide a general construction of these topological operators in the context of geometric engineering as branes wrapped on the homological cycles in the asymptotic boundary of the internal geometry. We illustrate this proposal by determining non-invertible 2-form symmetries in 6D superconformal field theories. Furthermore, by wrapping type IIB 7-brane on the entire asymptotic boundary of the internal manifold, we explicitly give a unified string-theoretic construction of two different types of field-theoretic non-invertible duality defects.