Surface defects in the D4 - D8 brane system

A new class of exact supersymmetric solutions is derived within minimal $d = 6$ $F(4)$ gauged supergravity. These flows are all characterized by a non-trivial radial profile for the 2-form gauge potential included into the supergravity multiplet. In particular three solutions within this class are featured by an $\mathrm{AdS}_3$ foliation of the 6d background and by an $\mathrm{AdS}_6$ asymptotic geometry. Secondly, considering the simplest example of these, we give its massive IIA uplift describing a warped solution of the type $\mathrm{AdS}_3\times S^2\times S^3$ fibered over two intervals $I_r \times I_{\xi}$ . We interpret this background as the near-horizon of a D4 $-$ D8 system on which a bound state D2 $-$ NS5 $-$ D6 ends producing a surface defect. Finally we discuss its holographic dual interpretation in terms of a $\mathcal{N} = (0, 4)$ SCFT$_2$ defect theory within the $\mathcal{N} = 2$ SCFT$_5$ dual to the $\mathrm{AdS}_6\times S^4$ massive IIA warped vacuum.