In this thesis, we discuss noninvertible symmetries in four and five dimensional supegravities and their corresponding noninvertible topological operators, in the context of the noglobal symmetry conjecture and its connection to the completeness of the spectrum. After discussing the simpler examples of fourdimensional axionMaxwell and fivedimensional Maxwell ChernSimons theories, we introduce N=2 supergravity in four dimensions and its ªgeneralized theta termsº which seem to break every possible 0form axionic symmetry in the scalar sector. We argue that there are noninvertible 0form symmetries that are not explicitly broken by these terms. The noglobal symmetry conjecture then implies the necessity of nonperturbative corrections due to fundamental instantons, consistently with what is expected from string theory models. After reviewing N=1 fivedimensional supergravity, we construct its noninvertible operator both from a purely fivedimensional point of view and, in Mtheory models, by dimensionally reducing the Mtheory noninvertible symmetry operator. Then, by further reducing the topological noninvertible operator obtained for the fivedimensional theory, we construct explicitly a 0form noninvertible symmetry for N=2 fourdimensional supergravity. In type IIA compactifications on CalabiYau threefolds, we show that perturbative corrections to the leading N=2 prepotential do not affect the noninvertible operator that we have obtained.
In this thesis, we discuss noninvertible symmetries in four and five dimensional supegravities and their corresponding noninvertible topological operators, in the context of the noglobal symmetry conjecture and its connection to the completeness of the spectrum. After discussing the simpler examples of fourdimensional axionMaxwell and fivedimensional Maxwell ChernSimons theories, we introduce N=2 supergravity in four dimensions and its ªgeneralized theta termsº which seem to break every possible 0form axionic symmetry in the scalar sector. We argue that there are noninvertible 0form symmetries that are not explicitly broken by these terms. The noglobal symmetry conjecture then implies the necessity of nonperturbative corrections due to fundamental instantons, consistently with what is expected from string theory models. After reviewing N=1 fivedimensional supergravity, we construct its noninvertible operator both from a purely fivedimensional point of view and, in Mtheory models, by dimensionally reducing the Mtheory noninvertible symmetry operator. Then, by further reducing the topological noninvertible operator obtained for the fivedimensional theory, we construct explicitly a 0form noninvertible symmetry for N=2 fourdimensional supergravity. In type IIA compactifications on CalabiYau threefolds, we show that perturbative corrections to the leading N=2 prepotential do not affect the noninvertible operator that we have obtained.
Noninvertible symmetries and quantum supergravities in 4 and 5 dimensions
GRIECO, ALESSANDRA
2022/2023
Abstract
In this thesis, we discuss noninvertible symmetries in four and five dimensional supegravities and their corresponding noninvertible topological operators, in the context of the noglobal symmetry conjecture and its connection to the completeness of the spectrum. After discussing the simpler examples of fourdimensional axionMaxwell and fivedimensional Maxwell ChernSimons theories, we introduce N=2 supergravity in four dimensions and its ªgeneralized theta termsº which seem to break every possible 0form axionic symmetry in the scalar sector. We argue that there are noninvertible 0form symmetries that are not explicitly broken by these terms. The noglobal symmetry conjecture then implies the necessity of nonperturbative corrections due to fundamental instantons, consistently with what is expected from string theory models. After reviewing N=1 fivedimensional supergravity, we construct its noninvertible operator both from a purely fivedimensional point of view and, in Mtheory models, by dimensionally reducing the Mtheory noninvertible symmetry operator. Then, by further reducing the topological noninvertible operator obtained for the fivedimensional theory, we construct explicitly a 0form noninvertible symmetry for N=2 fourdimensional supergravity. In type IIA compactifications on CalabiYau threefolds, we show that perturbative corrections to the leading N=2 prepotential do not affect the noninvertible operator that we have obtained.File  Dimensione  Formato  

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https://hdl.handle.net/20.500.12608/56228