Supersymmetric domain walls in 7D maximal gauged supergravity

Abstract

We give a large class of supersymmetric domain walls in maximal seven-dimensional gauged supergravity with various types of gauge groups. Gaugings are described by components of the embedding tensor transforming in representations $15$ and $\overline{40}$ of the global symmetry $SL(5)$. The embedding tensor in $15$ representation leads to $CSO(p,q,5-p-q)$ gauge groups while gaugings in $\overline{40}$ representation describes $CSO(p,q,4-p-q)$ gauge groups. These gaugings admit half-supersymmetric domain walls as vacuum solutions. On the other hand, gaugings involving both $15$ and $\overline{40}$ components lead to $\frac{1}{4}$-supersymmetric domain walls. In this case, the gauge groups under consideration are $SO(2,1)⋉{\mathbf{R}}^4$ and $CSO(2,0,2)\sim SO(2)⋉{\mathbf{R}}^4$. All of the domain wall solutions are analytically obtained. For $SO(5)$ gauge group, the gauged supergravity admits an $N=4$ supersymmetric $Ad{S}_7$ vacuum dual to $N=(2,0)$ SCFT in six dimensions. The corresponding domain walls can be interpreted as holographic RG flows from the $N=(2,0)$ SCFT to non-conformal $N=(2,0)$ field theories in the IR. The solutions can be uplifted to eleven dimensions by using a truncation ansatz on $S^4$. Furthermore, the gauged supergravity with $CSO(4,0,1)\sim SO(4)⋉{\mathbf{R}}^4$ gauge group can be embedded in type IIA theory via a truncation on $S^3$. The uplifted domain walls, describing NS5-branes of type IIA theory, are also given.

arXiv comment38 pages, no figures, typos corrected and references added

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• Twisted compactifications of 6D field theories from maximal 7D gauged supergravity
• Supersymmetric solutions of 7D maximal gauged supergravity
• Supersymmetric domain walls in maximal 6D gauged supergravity I
• Supersymmetric domain walls in maximal 6D gauged supergravity II
• Supersymmetric domain walls in maximal 6D gauged supergravity III
• Generalised U-dual solutions in supergravity