Supersymmetric domain walls in 7D maximal gauged supergravity

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} and overline{mathbf {40}} of the global symmetry SL(5). The embedding tensor in mathbf {15} representation leads to CSO(p,q,5-p-q) gauge groups while gaugings in overline{mathbf {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 mathbf {15} and overline{mathbf {40}} components lead to frac{1}{4}-supersymmetric domain walls. In this case, the gauge groups under consideration are SO(2,1)ltimes mathbf {R}^4 and CSO(2,0,2)sim SO(2)ltimes mathbf {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)sim SO(4)ltimes mathbf {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.