Universal properties of Kaluza-Klein gravitons

Abstract

Vacua of different gaugings of $D=4$ $\mathcal{N}=8$ supergravity that preserve the same supersymmetries and bosonic symmetry tend to exhibit the same universal mass spectrum within their respective supergravities. For AdS${}_4$ vacua in gauged supergravities that arise upon consistent truncation of string/M-theory, we show that this universality is lost at higher Kaluza-Klein levels. However, universality is still maintained in a milder form, as certain sums over a finite number of states remain universal. Further, we derive a mass matrix for Kaluza-Klein gravitons which is valid for all the AdS${}_4$ vacua in string/M-theory that uplift from the gaugings of $D=4$ $\mathcal{N}=8$ supergravity that we consider. The mild universality of mass sums is related to the trace of this mass matrix.

29 pages. v2: minor typos fixed and references added. Version to be published in JHEP