We give a large class of supersymmetric domain walls in maximal seven-dimensional gauged supergravity with various types of gauge groups. Gaugings are described by components of the embedding tensor transforming in representations 15 and 40 of the global symmetry SL(5). The embedding tensor in 15 representation leads to CSO(p, q, 5 − p − q) gauge groups while gaugings in 40 representation describes CSO(p, q, 4 − p − q) gauge groups. These gaugings admit half-supersymmetric domain walls as vacuum solutions. On the other hand, gaugings involving both 15 and 40 components lead to 1 4 -supersymmetric domain walls. In this case, the gauge groups under consideration are SO(2, 1) ⋉ R 4 and CSO(2, 0, 2) ∼ SO(2) ⋉ R 4 . All of the domain wall solutions are analytically obtained. For SO(5) gauge group, the gauged supergravity admits an N = 4 supersymmetric AdS 7 vacuum dual to N = (2, 0) SCFT in six dimensions. The corresponding domain walls can be interpreted as holographic RG flows from the N = (2, 0) SCFT to non-conformal N = (2, 0) field theories in the IR. The solutions can be uplifted to eleven dimensions by using a truncation ansatz on S 4 . Furthermore, the gauged supergravity with CSO(4, 0, 1) ∼ SO(4) ⋉ R 4 gauge group can be embedded in type IIA theory via a truncation on S 3 . The uplifted domain walls, describing NS5-branes of type IIA theory, are also given.

We study supersymmetric solutions within seven-dimensional N = 2 gauged supergravity coupled to three vector multiplets in seven dimensions. The gauged supergravity contains six vector fields that gauge the SO(4) ∼ SO(3) × SO(3) symmetry and admits two N = 2 supersymmetric AdS 7 vacua with SO(4) and SO(3) diag ⊂ SO(3) × SO(3) symmetries. We consider solutions interpolating between two asymptotically locally AdS 7 geometries in the presence of a three-form field. For a particular value of the two SO(3) gauge coupling constants, the SO(3) diag supersymmetric AdS 7 vacuum does not exist, but the solutions can be uplifted to eleven dimensions by a known reduction ansatz. We also study solutions of this type and their embedding in M-theory. We further extend these solutions to include the SO(3) diag gauge fields and argue that, in general, this generalization does not lead to supersymmetric solutions.

We study a number of supersymmetric solutions in the form of M kw 3 × S 3 -and AdS 3 × S 3 -sliced domain walls in the maximal gauged supergravity in seven dimensions. These solutions require non-vanishing three-form fluxes to support the AdS 3 and S 3 subspaces. We consider solutions with SO(4), SO(3), SO(2)×SO(2) and SO(2) symmetries in CSO(p, q, 5−p−q), CSO(p, q, 4 − p − q) and SO(2, 1) ⋉ R 4 gauge groups. All of these solutions can be analytically obtained. For SO(5) and CSO(4, 0, 1) gauge groups, the complete truncation ansatze in terms of eleven-dimensional supergravity on S 4 and type IIA theory on S 3 are known. We give the full uplifted solutions to eleven and ten dimensions in this case. The solutions with an AdS 3 × S 3 slice are interpreted as two-dimensional surface defects in sixdimensional N = (2, 0) superconformal field theory in the case of SO(5) gauge group or N = (2, 0) nonconformal field theories for other gauge groups. For SO(4) symmetric solutions, it is possible to find solutions with both the three-form fluxes and SO(3) gauge fields turned on. However, in this case, the solutions can be found only numerically. For SO(3) symmetric solutions, the three-form fluxes and SO(3) gauge fields cannot be non-vanishing simultaneously.

We study supersymmetric AdS n ×Σ 7−n , n = 2, 3, 4, 5 solutions in sevendimensional 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 • T 5−p−q and H p,q • T 4−p−q , respectively. Apart from recovering the previously known AdS n × Σ 7−n solutions in SO(5) gauge group, we find novel classes of AdS 5 × S 2 , AdS 3 × S 2 × Σ 2 and AdS 3 × CP 2 solutions in non-compact SO(3, 2) gauge group together with a class of AdS 3 × 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 × Σ 7−n fixed points and singular geometries in the form of curved domain walls with M kw n−1 × Σ 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 × Σ 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.

We continue our study of gaugings the maximal N = (2, 2) supergravity in six dimensions with gauge groups obtained from decomposing the embedding tensor under R + × SO(4, 4) subgroup of the global symmetry SO(5, 5). Supersymmetry requires the embedding tensor to transform in 144 c representation of SO(5, 5). Under R + × SO(4, 4) subgroup, this leads to the embedding tensor in (8 ±3 , 8 ±1 , 56 ±1 ) representations. Gaugings in 8 ±3 representations lead to a translational gauge group R 8 while gaugings in 8 ±1 representations give rise to gauge groups related to the scaling symmetry R + . On the other hand, the embedding tensor in 56 ±1 representations gives CSO(4 − p, p, 1) ∼ SO(4 − p, p) ⋉ R 4 ⊂ SO(4, 4) gauge groups with p = 0, 1, 2. More interesting gauge groups can be obtained by turning on more than one representation of the embedding tensor subject to the quadratic constraints. In particular, we consider gaugings in both 56 −1 and 8 +3 representations giving rise to larger SO(5 − p, p) and SO(4 − p, p + 1) gauge groups for p = 0, 1, 2. In this case, we also give a number of half-supersymmetric domain wall solutions preserving different residual symmetries. The solutions for gaugings obtained only from 56 −1 representation are also included in these results when the 8 +3 part is accordingly turned off.