Supersymmetric domain walls in 7D maximal gauged supergravity

Abstract

Abstract 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 $$\mathbf {15}$$ 15 and $$\overline{\mathbf {40}}$$ 40¯ of the global symmetry SL(5). The embedding tensor in $$\mathbf {15}$$ 15 representation leads to $$CSO(p,q,5-p-q)$$ CSO(p,q,5-p-q) gauge groups while gaugings in $$\overline{\mathbf {40}}$$ 40¯ representation describes $$CSO(p,q,4-p-q)$$ 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 $$\mathbf {15}$$ 15 and $$\overline{\mathbf {40}}$$ 40¯ components lead to $$\frac{1}{4}$$ 14 -supersymmetric domain walls. In this case, the gauge groups under consideration are $$SO(2,1)\ltimes \mathbf {R}^4$$ SO(2,1)⋉R4 and $$CSO(2,0,2)\sim SO(2)\ltimes \mathbf {R}^4$$ CSO(2,0,2)∼SO(2)⋉R4 . All of the domain wall solutions are analytically obtained. For SO(5) gauge group, the gauged supergravity admits an $$N=4$$ N=4 supersymmetric $$AdS_7$$ AdS7 vacuum dual to $$N=(2,0)$$ N=(2,0) SCFT in six dimensions. The corresponding domain walls can be interpreted as holographic RG flows from the $$N=(2,0)$$ N=(2,0) SCFT to non-conformal $$N=(2,0)$$ N=(2,0) field theories in the IR. The solutions can be uplifted to eleven dimensions by using a truncation ansatz on $$S^4$$ S4 . Furthermore, the gauged supergravity with $$CSO(4,0,1)\sim SO(4)\ltimes \mathbf {R}^4$$ CSO(4,0,1)∼SO(4)⋉R4 gauge group can be embedded in type IIA theory via a truncation on $$S^3$$ S3 . The uplifted domain walls, describing NS5-branes of type IIA theory, are also given.