We study a large class of domain wall solutions with $Mk{w}_3\times {\mathrm{\Sigma }}^2$ and $Mk{w}_2\times {\mathrm{\Sigma }}^3$ slices from maximal gauged supergravity in six dimensions. ${\mathrm{\Sigma }}^2$ and ${\mathrm{\Sigma }}^3$ are given by a Riemann surface and a three-manifold with constant curvature while $Mk{w}_{3,2}$ denotes three-/two-dimensional Minkowski space. We consider the maximal gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)⋉{\mathbb{R}}^4$ 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 ${\mathrm{\Sigma }}^2$ and ${\mathrm{\Sigma }}^3$, we find a number of solutions interpolating between locally flat domain walls in the UV and curved domain walls with $Mk{w}_3\times {\mathrm{\Sigma }}^2$ and $Mk{w}_2\times {\mathrm{\Sigma }}^3$ slices in the IR. Many solutions admit physical IR singularities and can be interpreted as holographic renormalization group (RG) flows across dimensions from five-dimensional field theories to three- and two-dimensional nonconformal field theories in the IR. Upon being uplifted to type IIA theory, we expect the solutions to describe brane configurations involving D4-branes wrapped on ${\mathrm{\Sigma }}^2$ and ${\mathrm{\Sigma }}^3$.

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• Gauge-gravity dualities
• Supergravity