Supersymmetric solutions of 7D maximal gauged supergravity

TL;DR

This paper classifies and constructs supersymmetric solutions in 7D maximal gauged supergravity with various symmetries, providing analytic solutions and uplifts to higher dimensions, and interprets some as surface defects in 6D superconformal theories.

Contribution

It offers a comprehensive set of analytic supersymmetric solutions with different symmetries and provides explicit uplift formulas, advancing understanding of 7D supergravity and its higher-dimensional origins.

Findings

All solutions with certain symmetries are analytically obtained.

Explicit uplifted solutions to 11D and 10D supergravity are provided.

Numerical solutions are found for some cases where analytic solutions are not possible.

Abstract

We study a number of supersymmetric solutions in the form of $Mkw_3\times S^3$- and $AdS_3\times S^3$-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 $SO(4)$, $SO(3)$, $SO(2)\times SO(2)$ and $SO(2)$ symmetries in $CSO(p,q,5-p-q)$, $CSO(p,q,4-p-q)$ and $SO(2,1)\ltimes \mathbf{R}^4$ 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 $AdS_3\times S^3$ slice are interpreted as two-dimensional surface defects in six-dimensional $N=(2,0)$ 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.