Domain walls in three dimensional gauged supergravity

Abstract

We explicitly construct two Chern-Simons gauged supergravities in three dimensions with N = 4 and N = 8 supersymmetries and non-semisimple gauge groups. The N = 4 theory has scalar manifold SO(4, 3)/SO(4) × SO(3) with the gauge group $\mathrm{SO}(3)\ltimes \left( {{{\mathbf{T}}^3},{{{\widehat{\mathbf{T}}}}^3}} \right)$. The theory describes (1, 0) six dimensional supergravity reduced on an SU(2) group manifold. The equivalent Yang-Mills type gauged supergravity has SO(3) gauge group coupled to three massive vector fields. The N = 8 theory is described by SO(8, 8)/SO(8) × SO(8) scalar manifold, and the gauge group is given by SO(8) ⋉ T ²⁸. The theory is a truncation of the SO(8) ⋉ T ²⁸ gauged N = 16 theory with scalar manifold E ₈₍₈₎/SO(16) and can be obtained by an S ⁷ compactification of type I theory in ten dimensions. Domain wall solutions of both gauged supergravities are analytically found and can be uplifted to higher dimensions. These provide domain wall vacua in the three dimensional gauged supergravity framework which might be useful for the study of Domain Wall₃/QFT₂ correspondence.