Supersymmetric solutions of seven-dimensional gauged supergravities and ads7/cft6 duality

Abstract

Describing quantum field theory using the AdS/CFT duality can broaden string theory applications in the context of the holographic principle. This research study supersymmetric solutions of matter-coupled SO(4) and maximal gauged supergravities in seven dimensions of which the dual field theories are sixdimensional superconformal field theories (SCFTs). We find a large class of domain wall (DW) solutions in the maximal theory with various gauge groups. For SO(5) gauge group admitting an AdS7 vacuum, the solutions describe holographic renormalization group (RG) flows from an N = (2, 0) SCFT to non-conformal field theories (SQFTs) in six dimensions. For other gauge groups without AdS7 vacua, these DWs are supersymmetric vacua dual to six-dimensional N = (2, 0) SQFTs. By coupling DWs to three-form fields, we find charged DW solutions in both theories. The solutions with AdS3 × S 3 slices are interpreted as conformal surface defects within the dual field theories in six dimensions. We also find twisted solutions describing holographic RG flows across dimensions from six-dimensional field theories to SCFTs in lower dimensions. We consider solutions of the mattercoupled theory in the presence of a three-form field and extend twisted solutions of the maximal theory to include singularities in the form of curved DWs. In many cases, these singularities are physically acceptable and can be interpreted as SQFTs in lower dimensions. Many solutions can be uplifted to ten and eleven dimensions resulting in new classes of solutions in string and M-theories.