on a hyperbolic Riemann surface, the central charges are positive, which is compatible with unitary and suggests that the fixed points indeed exist. However, with only $(0,2)$ supersymmetry in two-dimensions, it is typically difficult to establish rigorously the existence of a fixed point in the IR.[^1] One way to obtain more evidence for the existence of the IR fixed points is to construct string theory or supergravity backgrounds which are holographic duals to the field theories of interest. This is one of the tools we will utilize in our work. To this end we find new supersymmetric $AdS_3 \times \Sigma_{\mathfrak{g}}$ supergravity solutions in the spirit of [@Maldacena:2000mw; @Benini:2012cz; @Benini:2013cda; @Bah:2011vv; @Bah:2012dg]. In addition, we construct numerical solutions which we interpret as holographic RG flows from an asymptotically locally $AdS_5$ solution to the $AdS_3 \times \Sigma_{\mathfrak{g}}$ vacua of interest. This shows that, at least in the regime of validity of holography, the RG flows are realized dynamically.

The paper is organized as follows. In Section \[Sec:FieldTheory\] we summarize the salient features of the $\mathcal{N}=1$ LS SCFT. We then put the theory on $\mathbb{R}^{1,1}\times \Sigma_{\mathfrak{g}}$, perform a partial topological twist and calculate the conformal anomaly of the resulting family of two-dimensional $(0,2)$ 