Supersymmetric domain walls in maximal 6D gauged supergravity III

Abstract

We continue our study of gaugings the maximal $$N=(2,2)$$ N = ( 2 , 2 ) supergravity in six dimensions with gauge groups obtained from decomposing the embedding tensor under $${\mathbb {R}}^+\times SO(4,4)$$ R + × S O ( 4 , 4 ) subgroup of the global symmetry SO(5, 5). Supersymmetry requires the embedding tensor to transform in $${\textbf{144}}_c$$ 144 c representation of SO(5, 5). Under $${\mathbb {R}}^+\times SO(4,4)$$ R + × S O ( 4 , 4 ) subgroup, this leads to the embedding tensor in $$({\textbf{8}}^{\pm 3},$$ ( 8 ± 3 , $${\textbf{8}}^{\pm 1},{\textbf{56}}^{\pm 1})$$ 8 ± 1 , 56 ± 1 ) representations. Gaugings in $${\textbf{8}}^{\pm 3}$$ 8 ± 3 representations lead to a translational gauge group $${\mathbb {R}}^8$$ R 8 while gaugings in $${\textbf{8}}^{\pm 1}$$ 8 ± 1 representations give rise to gauge groups related to the scaling symmetry $${\mathbb {R}}^+.$$ R + . On the other hand, the embedding tensor in $${\textbf{56}}^{\pm 1}$$ 56 ± 1 representations gives $$CSO(4-p,p,1)\sim SO(4-p,p) < imes {\mathbb {R}}^4\subset SO(4,4)$$ C S O ( 4 - p , p , 1 ) ∼ S O ( 4 - p , p ) ⋉ R 4 ⊂ S O ( 4 , 4 ) gauge groups with $$p=0,1,2.$$ p = 0 , 1 , 2 . More interesting gauge groups can be obtained by turning on more than one representation of the embedding tensor subject to the quadratic constraints. In particular, we consider gaugings in both $${\textbf{56}}^{-1}$$ 56 - 1 and $${\textbf{8}}^{+3}$$ 8 + 3 representations giving rise to larger $$SO(5-p,p)$$ S O ( 5 - p , p ) and $$SO(4-p,p+1)$$ S O ( 4 - p , p + 1 ) gauge groups for $$p=0,1,2.$$ p = 0 , 1 , 2 . In this case, we also give a number of half-supersymmetric domain wall solutions preserving different residual symmetries. The solutions for gaugings obtained only from $${\textbf{56}}^{-1}$$ 56 - 1 representation are also included in these results when the $${\textbf{8}}^{+3}$$ 8 + 3 part is accordingly turned off.