Supersymmetric domain walls in maximal 6D gauged supergravity I

Abstract

Abstract We find a large class of supersymmetric domain wall solutions from six-dimensional $$N=(2,2)$$ N = ( 2 , 2 ) gauged supergravity with various gauge groups. In general, the embedding tensor lives in $${{\mathbf {144}}}_c$$ 144 c representation of the global symmetry SO(5, 5). We explicitly construct the embedding tensors in $${{\mathbf {15}}}^{-1}$$ 15 - 1 and $$\overline{{\mathbf {40}}}^{-1}$$ 40 ¯ - 1 representations of $$GL(5)\sim {\mathbb {R}}^+\times SL(5)\subset SO(5,5)$$ G L ( 5 ) ∼ R + × S L ( 5 ) ⊂ S O ( 5 , 5 ) leading to $$CSO(p,q,5-p-q)$$ C S O ( p , q , 5 - p - q ) and $$CSO(p,q,4-p-q)\ltimes {\mathbb {R}}^4_{{\varvec{s}}}$$ C S O ( p , q , 4 - p - q ) ⋉ R s 4 gauge groups, respectively. These gaugings can be obtained from $$S^1$$ S 1 reductions of seven-dimensional gauged supergravity with $$CSO(p,q,5-p-q)$$ C S O ( p , q , 5 - p - q ) and $$CSO(p,q,4-p-q)$$ C S O ( p , q , 4 - p - q ) gauge groups. As in seven dimensions, we find half-supersymmetric domain walls for purely magnetic or purely electric gaugings with the embedding tensors in $${{\mathbf {15}}}^{-1}$$ 15 - 1 or $$\overline{{\mathbf {40}}}^{-1}$$ 40 ¯ - 1 representations, respectively. In addition, for dyonic gauge groups with the embedding tensors in both $${{\mathbf {15}}}^{-1}$$ 15 - 1 and $$\overline{{\mathbf {40}}}^{-1}$$ 40 ¯ - 1 representations, the domain walls turn out to be $$\frac{1}{4}$$ 1 4 -supersymmetric as in the seven-dimensional analogue. By the DW/QFT duality, these solutions are dual to maximal and half-maximal super Yang–Mills theories in five dimensions. All of the solutions can be uplifted to seven dimensions and further embedded in type IIB or M-theories by the well-known consistent truncation of the seven-dimensional $$N=4$$ N = 4 gauged supergravity.