Gauging CSO groups in N=4 Supergravity

TL;DR

<3-5 sentence high-level summary>We study CSO gaugings of $\mathcal{N}=4$ supergravity with six vector multiplets by constructing invariant metrics on $\mathfrak{cso}(p,q,r)$ and embedding them into $SO(6,6)$, then analyzing the scalar potential with respect to both $SU(1,1)$ and $SO(6,6)$ sectors at the point $Z_0$ where matter is off. The extremization procedure reveals that no gauging yields a fully stable vacuum in the full scalar sector, even though a simultaneous extremum exists for certain CSO combinations, these remain unstable in the matter directions. Importantly, a stable cosmological scaling solution is found for $CSO(1,1,2)$ (and powers), with an effective potential $V_{ m eff}(\\chi) \propto e^{\chi}$ and a scale factor $a(t) \propto t^{1/b^2}$, highlighting a viable cosmological regime within this gauged $\mathcal{N}=4$ framework.

Abstract

We investigate a class of CSO-gaugings of N=4 supergravity coupled to six vector multiplets. Using the CSO-gaugings we do not find a vacuum that is stable against all scalar perturbations at the point where the matter fields are turned off. However, at this point we do find a stable cosmological scaling solution.