The complete N=3 Kaluza Klein spectrum of 11D supergravity on AdS_4 x N^{010}

TL;DR

This work derives the complete Kaluza–Klein spectrum of eleven-dimensional supergravity on $AdS_4\times N^{010}$ with ${\cal N}=3$ supersymmetry by performing harmonic analysis on the coset $N^{010}=\frac{SU(3)\times SU(2)}{SU(2)\times U(1)}$. It constructs invariant mass operators for the 0-, 1-, 2-forms and spinor, computes their eigenvalues across all $SU(3)\times SO(3)$ representations, and shows how these data reproduce the full ${\cal N}=3$ multiplet structure, including the massless graviton multiplet, the Betti multiplet, and the SU(3) Killing vector multiplet. The paper also explains shortening mechanisms that occur when unitarity bounds are saturated and provides a systematic framework to obtain the complete spectrum, setting the stage for detailed AdS$_4$/CFT$_3$ checks in this background. Overall, the results furnish an explicit, group-theory–driven spectrum for a nontrivial Freund–Rubin compactification, enabling precise tests of holography in this ${\cal N}=3$ context.

Abstract

We derive the invariant operators of the zero-form, the one-form, the two-form and the spinor from which the mass spectrum of Kaluza Klein of eleven-dimensional supergravity on AdS_4 x N^{010} can be derived by means of harmonic analysis. We calculate their eigenvalues for all representations of SU(3)xSO(3). We show that the information contained in these operators is sufficient to reconstruct the complete N=3 supersymmetry content of the compactified theory. We find the N=3 massless graviton multiplet, the Betti multiplet and the SU(3) Killing vector multiplet.