Spin 2 operators in holographic 4d $\mathcal N=2$ SCFTs

A broad class of holographic duals for 4d $\mathcal N=2$ SCFTs is based on the general half-BPS $AdS_5$ solutions to M-theory constructed by Lin, Lunin and Maldacena, and their Kaluza-Klein reductions to Type IIA. We derive the equations governing spin 2 fluctuations around these solutions. The resulting partial differential equations admit families of universal solutions which are constructed entirely out of the generic data characterizing the background. This implies the existence of families of spin 2 operators in the dual SCFTs, in short superconformal multiplets which we identify.