KPW point, which is the holographic dual of the $\mathcal{N}=1$ LS SCFT [@Freedman:1999gp; @Khavaev:1998fb; @Karch:1999pv]. In particular, within the truncation , we will be interested in constructing supersymmetric flows that, in a certain sense,[^7] interpolate between this point and supersymmetric solutions of the form $AdS_3\times \Sigma_\mathfrak{g}$.

It might be worth pointing out that the five-dimensional theory used in [@Maldacena:2000mw; @Benini:2012cz; @Benini:2013cda] to find similar supersymmetric flows from the maximally supersymmetric $SO(6)$ point to $AdS_3\times \Sigma_\mathfrak{g}$ solutions is a truncation of obtained by setting $\chi=\theta=0$. This truncation is usually called the STU model of five-dimensional gauged supergravity [@Cvetic:1999xp].

The Ansatz
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We will assume from now on that the metric on the Riemann surface, $\Sigma_{\frak g}$, has the constant curvature. This is justified if we extrapolate the result in [@Anderson:2011cz], where it was shown that the holographic RG flow uniformizes the metric on a Riemann surface for the supergravity truncation with $\chi=0$. We have checked that for $\mathfrak{g}=0,1$ there are no supersymmetric $AdS_3\times \Sigma_\mathfrak{g}$ solutions and, to simplify the presentation, we will assume from now on that $\frak g>1$. The Riemann surface $\Sigma_{\mathfrak{g}}$ can then be represented as a quotient of the upper half plane with the metric, $$\label{}
ds^2_{\mathbb{H}_2}\eql {1\over 