Kaluza-Klein spectroscopy from exceptional field theory

The spectrum of single-trace operators of holographic CFTs at strong coupling and large N can be mapped to the spectrum of Kaluza-Klein (KK) excitations over the dual AdS supergravity solutions. Unfortunately, computing these KK spectra is usually a prohibitively difficult task even for the simplest AdS solutions. In this talk, I will review new spectral methods based on Exceptional Field Theory that, for certain AdS/CFT dual pairs, bypass all difficulties and reduce the KK spectral problem to a simple diagonalisation of suitable mass matrices. I will illustrate these methods for the class of AdS4 solutions of M-theory and type II string theory that uplift consistently from D=4 maximal gauged supergravities. Also, I will describe progress to extend these methods to AdS solutions that uplift from half-maximal supergravities.