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

We study supersymmetric AdS${}_n$$\times$ Σ${}^{7\text{â}\text{ˆ}\text{’}n}$, n=2,3,4,5 solutions in seven-dimensional maximal gauged supergravity with CSO(p,q,5−p−q) and CSO(p,q,4−p−q) gauge groups. These gauged supergravities are consistent truncations of eleven-dimensional supergravity and type IIB theory on H${}^{p,q}$$\circ$ T${}^{5\text{â}\text{ˆ}\text{’}p\text{â}\text{ˆ}\text{’}q}$ and H${}^{p,q}$$\circ$ T${}^{4\text{â}\text{ˆ}\text{’}p\text{â}\text{ˆ}\text{’}q}$, respectively. Apart from recovering the previously known AdS${}_n$$\times$ Σ${}^{7\text{â}\text{ˆ}\text{’}n}$ solutions in SO(5) gauge group, we find novel classes of AdS${}_5$$\times$ S${}^2$, AdS${}_3$$\times$ S${}^2$$\times$ Σ${}^2$ and AdS${}_3$$\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$ Σ${}^{7\text{â}\text{ˆ}\text{’}n}$ fixed points and singular geometries in the form of curved domain walls with Mkw${}_{n\text{â}\text{ˆ}\text{’}1}$$\times$ Σ${}^{7\text{â}\text{ˆ}\text{’}n}$ slices. In many cases, the singularities are physically acceptable and can be interpreted as non-conformal phases of (n−1)-dimensional SCFTs obtained from twisted compactifications of N=(2,0) SCFT in six dimensions. In SO(3, 2) and SO(4, 1) gauge groups, we give a large number of RG flows between the new AdS${}_n$$\times$ Σ${}^{7\text{â}\text{ˆ}\text{’}n}$ 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.