Wrapped D4-branes from maximal 6D gauged supergravity

We study a large class of domain wall solutions with $Mkw_3\times \Sigma^2$ and $Mkw_2\times \Sigma^3$ slices from maximal gauged supergravity in six dimensions. $\Sigma^2$ and $\Sigma^3$ are given by a Riemann surface and a $3$-manifold with constant curvature while $Mkw_{3,2}$ denotes three/two-dimensional Minkowski space. We consider the maximal gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)\ltimes \mathbb{R}^4$ gauge groups arising from an $S^1$ reduction of seven-dimensional maximal gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)$ gauge groups. The two types of gauge group can be embedded in type IIA theory via consistent truncations on $H^{p,q}\times \mathbb{R}^{5-p-q}$ and $H^{p,q}\times\mathbb{R}^{4-p-q}\times S^1$, respectively. By performing topological twists on $\Sigma^2$ and $\Sigma^3$, we find a number of solutions interpolating between locally flat domain walls in the UV and curved domain walls with $Mkw_3\times \Sigma^2$ and $Mkw_2\times \Sigma^3$ slices in the IR. Many solutions admit physical IR singularities and can be interpreted as holographic RG flows across dimensions from five-dimensional field theories to three- and two-dimensional non-conformal field theories in the IR. Upon uplifted to type IIA theory, we expect the solutions to describe brane configurations involving D4-branes wrapped on $\Sigma^2$ and $\Sigma^3$.