Spectroscopy and truncations from holography and exceptional dualities

This thesis explores the relation between theories in different dimensions, focusing on the physics of string theory compactifications down to $D=4$. We consider the limit in which the higher-dimensional theories are described by $D=11$ or type II supergravity, and the studied solutions contain an AdS$_4$ factor and are thus relevant for holography.

The two main objects of study are Kaluza-Klein (KK) spectroscopy and consistent truncations. The first consists in the study of the features of the infinite towers of modes resulting from the compactification, whose properties are controlled by the choice of fluxes and geometry on the internal space. The latter are situations in which we can reduce these towers to a finite subset of modes whose dynamics is given by a lower-dimensional supergravity which can be consistently embedded into the higher-dimensional counterpart.

After discussing the compactifications on tori as an introductory example to present the relevant concepts, we will analyse each topic in separate parts. In the first part, we explain how progress has been made in obtaining consistent truncations based on supersymmetry and $G$-structures, and on the duality groups governing the lower-dimensional supergravities thanks to the tensor and duality hierarchies and Exceptional Field Theory (ExFT). The second part addresses KK spectroscopy and its importance to holography. Until very recently, on non-homogeneous solutions only tools to study the spin-2 sector were available. These tools are combined with group theory to examine the configuration dual to the IR SCFT of a relevant deformation of the theory in the worldvolume of a stack of M2 branes. Subsequently, we show how these methods can be extended to lower-spin fields within the ExFT framework, and use them to analyse different classes of solutions in $D=10$ and $D=11$ of holographic interest.