Supersymmetric spectroscopy on AdS$_4\times S^7$ and AdS$_4\times S^6$

Understand

New techniques based on Exceptional Field Theory have recently allowed for the calculation of the Kaluza-Klein spectra of certain AdS$_4$ solutions of $D=11$ and massive IIA supergravity.

• These are the solutions that consistently uplift on $S^7$ and $S^6$ from vacua of maximal four-dimensional supergravity with SO(8) and ISO(7) gaugings.
• In this paper, we provide the complete Kaluza-Klein spectrum of five such AdS$_4$ solutions, all of them ${\cal N}=1$.
• These solutions preserve SO(3) and $\textrm{U}(1) \times \textrm{U}(1)$ internal symmetry in $D=11$, and U(1) (two of them) and no continuous symmetry in type IIA.