Non-invertible symmetries and dualities in Type IIB supergravity

Type IIB supergravity bosonic pseudo-action exhibits a variety of global symmetries. In this thesis we study them within the formalism of generalized symmetries. Particular attention is dedicated to the 0-form symmetry SL(2,R), broken at the quantum level to SL(2,Z) due to the quantization of the fluxes of the 2-form fields. We find that interestingly a larger symmetry group SL(2,Q) survives as a non-invertible symmetry. The topological defects associated with this symmetry are constructed. The higher-form symmetries of the theory are analyzed as well: we build their corresponding symmetry defects and highlight their non-invertible nature through their action on charged operators. Finally, we exploit this non-invertible symmetry structure to derive inequalities constraining the hierarchy of energy scales at which the different symmetries of Type IIB supergravity must be broken in any consistent ultraviolet completion, in accordance with the No Global Symmetry Conjecture.