find a dual gravity description of the SCFTs and RG flows discussed in Section \[Sec:FieldTheory\]. In this section we identify a suitable truncation of $\cN=8$, $d=5$ gauged supergravity [@PPvN; @Gunaydin:1984qu; @Gunaydin:1985cu] and derive the corresponding BPS equations.

The truncation
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By the AdS/CFT correspondence, the $SO(6)$ gauge symmetry of $\cN=8$, $d=5$ gauged supergravity can be identified with the $R$-symmetry of $\cN=4$ SYM. We are interested in a truncation of this theory which is invariant under $U(1)_R\times U(1)_F\subset SO(6)$, where $U(1)_R$ is the $R$-symmetry of the LS fixed point and $U(1)_F\subset SU(2)_\ell$ is the flavor symmetry . The bosonic fields of $\cN=8$, $d=5$ gauged supergravity invariant under this subgroup of $SO(6)$ are: the metric, $g_{\mu\nu}$, three vector fields, $A^{(i)}$, $i=1,2,3$, gauging the $SO(2)_1\times SO(2)_2\times SO(2)_3$ subgroup in $ SO(6)$, and six scalar fields parametrizing the coset $$\label{slcosetM}
\mathcal{M} = O(1,1)\times O(1,1) \times  \dfrac{SU(2,1)}{SU(2)\times U(1)}\,.$$ Details of this truncation are discussed in Appendix \[appendixA\]. Here let us note that the scalar fields, $\alpha$ and $\beta$, parametrizing the first two factors in , come from the scalars in $\bf{20}'$ of $SO(6)$ and are dual to the bosonic bilinear operators $$\label{N=4ops}
\begin{split}
\mathcal{O}_{\alpha} &= {\rm Tr}\big(2\,|\phi_1|^2-|\phi_2|^2 - |\phi_3|^2\big)\;, \\[6 pt]
\mathcal{O}_{\beta} &= {\rm Tr}\big(\,|\phi_2|^2 