Universal properties of Kaluza-Klein gravitons

TL;DR

This paper investigates the universal properties of Kaluza-Klein gravitons in AdS4 vacua from string/M-theory, revealing that while individual mass spectra vary at higher levels, certain sums over states remain universal, and provides a general mass matrix applicable to these vacua.

Contribution

It introduces a mass matrix for Kaluza-Klein gravitons valid across all relevant AdS4 vacua and clarifies the conditions under which universality of mass sums persists.

Findings

Universal mass spectrum at low levels within supergravity vacua.

Loss of universality at higher Kaluza-Klein levels.

Existence of universal sums over finite states.

Abstract

Vacua of different gaugings of $D=4$ ${\cal N}=8$ 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 $D=4$ ${\cal N}=8$ supergravity that we consider. The mild universality of mass sums is related to the trace of this mass matrix.