Twisted compactifications of 6D field theories from maximal 7D gauged supergravity

We study supersymmetric $AdS_n\times \Sigma^{7-n}$, $n=2,3,4,5$ solutions in seven-dimensional maximal gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)$ gauge groups. These gauged supergravities are consistent truncations of eleven-dimensional supergravity and type IIB theory on $H^{p,q}\circ T^{5-p-q}$ and $H^{p,q}\circ T^{4-p-q}$, respectively. Apart from recovering the previously known $AdS_n\times \Sigma^{7-n}$ solutions in $SO(5)$ gauge group, we find novel classes of $AdS_5\times S^2$, $AdS_3\times S^2\times \Sigma^2$ and $AdS_3\times CP^2$ solutions in non-compact $SO(3,2)$ gauge group together with a class of $AdS_3\times CP^2$ solutions in $SO(4,1)$ gauge group. In $SO(5)$ gauge group, we extensively study holographic RG flow solutions interpolating from the $SO(5)$ supersymmetric $AdS_7$ vacuum to the $AdS_n\times \Sigma^{7-n}$ fixed points and singular geometries in the form of curved domain walls with $Mkw_{n-1}\times \Sigma^{7-n}$ slices. In many cases, the singularities are physically acceptable and can be interpreted as non-conformal phases of $(n-1)$-dimensional SCFTs obtained from twisted compactifications of $N=(2,0)$ SCFT in six dimensions. In $SO(3,2)$ and $SO(4,1)$ gauge groups, we give a large number of RG flows between the new $AdS_n\times \Sigma^{7-n}$ fixed points and curved domain walls while, in $CSO(p,q,4-p-q)$ gauge group, RG flows interpolating between asymptotically locally flat domain walls and curved domain walls are given.