y^2}\left({dx^2+dy^2}\right)\,,$$ by a discrete subgroup of $PSL(2,\RR)$. This makes our choice of a constant curvature metric manifest.

To find the supergravity solutions dual to the SCFTs in Section \[Sec:FieldTheory\], we employ the same Ansatz as in [@Maldacena:2000mw; @Benini:2012cz; @Benini:2013cda], where the metric is of the form $$\label{}
ds^2 = e^{2f(r)}(dt^2-dz^2-dr^2)-{e^{2h(r)}\over y^2}(dx^2+dy^2)\,,$$ with two undetermined functions, $f(r)$ and $h(r)$, of the radial coordinate, $r$. This metric Ansatz encompasses two types of solutions we are interested in: (i) asymptotically locally $AdS_5$ solutions[^8] with $\mathbb{R}^{1,1}\times \Sigma_{\frak{g}}$ boundary and $f(r)\sim h(r)\sim-\log r$ diverging at the same rate for $r\rightarrow 0$, and (ii) $AdS_3\times \Sigma_\mathfrak{g}$ solutions with constant $h(r)$ and divergent $f(r)\sim -\log r$ for $r\rightarrow\infty $. When needed, we adopt the obvious choice of frames $$\label{framedef}
e^{0} = e^{f(r)}dt\;, \qquad e^{1} = e^{f(r)}dz\;, \qquad e^{2} = e^{f(r)}dr\;, \qquad e^{3} = \frac{e^{h(r)}}{y}dx\;, \qquad e^{4} = \frac{e^{h(r)}}{y}dy\;.$$ The topological twist in the dual field theory implies that the flux of the gauge field on the gravity side must be proportional to the volume of the Riemann surface, $$\label{theflux}
F^{(i)}~\equiv~ dA^{(i)}\eql a_i\,{\rm vol}_{\Sigma_{\mathfrak g}}\,,\qquad {\rm vol}_{\Sigma_{\mathfrak g}}\eql {1\over y^2}\,dx\wedge dy \,,\qquad i=1,2,3\,,$$ where $a_i$ are arbitrary constants. Correspondingly, we take the gauge field potentials to be $$\label{}
