GENERALIZED SYMMETRIES IN SUPERGRAVITIES AND SUPERCONFORMAL FIELD THEORIES VIA STRING THEORY
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Graduate group
Discipline
Mathematics
Subject
Geometric Engineering
Quantum Field Theory
String Landscape
String Theory
Superconformal Field Theories
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Abstract
In this Dissertation, we study the generalized symmetries in supergravities and superconformal field theories from the string theory perspective. This thesis consists of two parts: Part one is devoted to the study of string universality, namely the question of whether all consistent quantum theories of gravity come from string theory. Answering this question requires us to combine the "top-down" approach of string compactifications and the "bottom-up" approach of anomalies. 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 (encoding the data of extended objects) and frozen singularities (capturing some non-geometric regime of string compactification). 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 and see that they rule out many global structures of the gauge group in 8D supergravity theory that do not admit a string theory construction. By combining these two approaches, our study provides strong evidence of string universality in high spacetime dimensions. Part two studies the generalized global symmetries of geometrically-engineered quantum field theories via string theory. We analyze some concrete string compactification scenarios, where branes wrapped on relative topological cycles give heavy defects in the quantum field theory that are charged under generalized global symmetries. We can also obtain generalized symmetries of a geometrically engineered QFT using bottom-up analysis, which can then be used to construct new lower-dimensional theories. By investigating the string theory origin of the topological operators (which are the definitions of generalized global symmetries), 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.
Advisor
Heckman, Jonathan, J.