Title: Logarithmic corrections in AdS/CFT
Abstract: In this talk, I will review the heat kernel formalism and explain how it can be used to compute logarithmic terms in the semi-classical expansion of supergravity observables due to one-loop effects. When applied to holographic Kaluza-Klein supergravity theories with a known spectrum, this method produces results that can be matched to the logarithmic terms in the large N expansion of the dual CFT observables. When available, our results are also compatible with one-loop computations in 11d supergravity and in supergravity localization. Reverting the logic, a mild assumption on the coefficient of log N terms in CFT observables yields strong constraints on the spectrum of arbitrary gravity theories in order for them to be compatible with AdS/CFT at the quantum level.