Searching for surface defect CFTs within AdS${}_3$

We study $$\mathrm{A}\mathrm{d}\mathrm{S}$_3\times S^3/$\mathbb{Z}$k\times {\tilde S}^3/$\mathbb{Z}${k’}$solutionstoM-theorypreserving$$\mathcal{N}$=(0,4)$ supersymmetries, arising as near-horizon limits of M2-M5 brane intersections ending on M5’-branes, with both types of five-branes placed on A-type singularities. Solutions in this class asymptote locally to ${\mathrm{A}\mathrm{d}\mathrm{S}}_7\mathrm{/}{\mathbb{Z}}_k\times {\tilde{S}}^3\mathrm{/}{\mathbb{Z}}_{k^{\mathrm{\prime }}}$, and can thus be interpreted as holographic duals to surface defect CFTs within the $\mathcal{N}=(1,0)$ 6d CFT dual to this solution. Upon reduction to Type IIA, we obtain a new class of solutions of the form $$\mathrm{A}\mathrm{d}\mathrm{S}$_3\times S^3/$\mathbb{Z}$_k\times S^2 \times \Sigma_2$ preserving (0,4) supersymmetries. We construct explicit 2d quiver CFTs dual to these solutions, describing D2-D4 surface defects embedded within the 6d (1,0) quiver CFT dual to the ${\mathrm{A}\mathrm{d}\mathrm{S}}_7\mathrm{/}{\mathbb{Z}}_k$ solution to massless IIA. Finally, in the massive case, we show that the recently constructed $$\mathrm{A}\mathrm{d}\mathrm{S}$_3\times S^2\times $\mathrm{C}\mathrm{Y}$_2$solutionswith$$\mathcal{N}$=(0,4)$ supersymmetries gain a defect interpretation when ${\mathrm{C}\mathrm{Y}}_2=T^4$ as surface CFTs originating from D2-NS5-D6 defects embedded within the 5d CFT dual to the Brandhuber-Oz ${\mathrm{A}\mathrm{d}\mathrm{S}}_6$ background.