Domain walls in three dimensional gauged supergravity

TL;DR

This paper constructs explicit three-dimensional gauged supergravity models with N=4 and N=8 supersymmetries, finds their domain wall solutions, and discusses their potential relevance for holographic dualities involving two-dimensional quantum field theories.

Contribution

It introduces new explicit models of gauged supergravity with non-semisimple gauge groups and constructs their domain wall solutions, extending the understanding of lower-dimensional supergravity theories.

Findings

Explicit N=4 and N=8 gauged supergravity models constructed.

Analytic domain wall solutions found and uplifted to higher dimensions.

Potential applications in Domain Wall$_3$/QFT$_2$ holographic correspondence.

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 $SO(4,3)/SO(4)\times SO(3)$ with the gauge group $SO(3)\ltimes (\mathbf{T}^3,\hat{\mathbf{T}}^3)$. 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 $SO(8,8)/SO(8)\times SO(8)$ scalar manifold, and the gauge group is given by $SO(8)\ltimes \mathbf{T}^{28}$. The theory is a truncation of the $SO(8)\ltimes \mathbf{T}^{28}$ 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 Wall$_3$/QFT$_2$ correspondence.