I will present a powerful new method that for the first time allows us to compute the Kaluza-Klein spectrum of a large class of string theory compactifications, including those arising in maximal gauged supergravities and beyond. This includes geometries with little to no remaining (super-)symmetries, completely inaccessible by previous methods.
I will show how these insights can be used to holographically compute the anomalous dimensions of protected and unprotected operators in strongly-coupled CFTs, as well as to study global properties of their conformal manifolds.
I will also show how the method can be used to determine the perturbative stability of non-supersymmetric AdS vacua. We will see the importance of higher Kaluza-Klein modes to the physics of string compactifications, e.g. in realising the compactness of moduli spaces, and in destabilising vacua that appear to stable in lower-dimensional supergravities.
If time permits, I will comment on ongoing work extending these methods to capturing cubic interactions in supergravity, where we will encounter a surprising new structure that is inherited from the consistent truncation to maximal gauged supergravity.
