Supersymmetric domain walls in maximal 6D gauged supergravity II

TL;DR

This paper classifies gauge groups and constructs supersymmetric domain wall solutions in six-dimensional maximal gauged supergravity, revealing new non-semisimple gauge groups and explicit domain wall configurations with specific symmetries.

Contribution

It provides a comprehensive classification of gauge groups via the embedding tensor and constructs explicit supersymmetric domain wall solutions in 6D supergravity.

Findings

Classified gauge groups with specific embedding tensors.

Constructed 1/2- and 1/4-supersymmetric domain walls.

Identified gauge groups with particular symmetry properties.

Abstract

We continue the study of supersymmetric domain wall solutions in six-dimensional maximal gauged supergravity. We first give a classification of viable gauge groups with the embedding tensor in $\mathbf{5}^{+7}$, $\bar{\mathbf{5}}^{+3}$, $\mathbf{10}^{-1}$, $\mathbf{24}^{-5}$, and $\overline{\mathbf{45}}^{+3}$ representations of the off-shell symmetry $GL(5)\subset SO(5,5)$. We determine an explicit form of the embedding tensor for gauge groups arising from each representation together with some examples of possible combinations among them. All of the resulting gauge groups are of a non-semisimple type with abelian factors and translational groups of different dimensions. We find $\frac{1}{2}$- and $\frac{1}{4}$-supersymmetric domain walls with $SO(2)$ symmetry in $SO(2)\ltimes \mathbb{R}^8$ and $SO(2)\ltimes \mathbb{R}^6$ gauge groups from the embedding tensor in $\mathbf{24}^{-5}$ representation and in $CSO(2,0,2)\ltimes \mathbb{R}^4$, $CSO(2,0,2)\ltimes \mathbb{R}^2$, and $CSO(2,0,1)\ltimes \mathbb{R}^4$ gauge groups with the embedding tensor in $\overline{\mathbf{45}}^{+3}$ representations. These gauge groups are parametrized by a traceless matrix and electrically and magnetically embedded in $SO(5,5)$ global symmetry, respectively.