RG flows from (1,0) 6D SCFTs to N=1 SCFTs in four and three dimensions

Abstract

We study $Ad{S}_5\times {\Sigma }_2$ and $Ad{S}_4\times {\Sigma }_3$ solutions of $N=2$, $SO(4)$ gauged supergravity in seven dimensions with ${\Sigma }_{2,3}$ being $S^{2,3}$ or $H^{2,3}$. The $SO(4)$ gauged supergravity is obtained from coupling three vector multiplets to the pure $N=2$, $SU(2)$ gauged supergravity. With a topological mass term for the 3-form field, the $SO(4)\sim SU(2)\times SU(2)$ gauged supergravity admits two supersymmetric $Ad{S}_7$ critical points, with $SO(4)$ and $SO(3)$ symmetries, provided that the two $SU(2)$ gauge couplings are different. These vacua correspond to $N=(1,0)$ superconformal field theories (SCFTs) in six dimensions. In the case of ${\Sigma }_2$, we find a class of $Ad{S}_5\times S^2$ and $Ad{S}_5\times H^2$ solutions preserving eight supercharges and $SO(2)\times SO(2)$ symmetry, but only $Ad{S}_5\times H^2$ solutions exist for $SO(2)$ symmetry. These should correspond to some $N=1$ four-dimensional SCFTs. We also give RG flow solutions from the $N=(1,0)$ SCFTs in six dimensions to these four-dimensional fixed points including a two-step flow from the $SO(4)$ $N=(1,0)$ SCFT to the $SO(3)$ $N=(1,0)$ SCFT that eventually flows to the $N=1$ SCFT in four dimensions. For $Ad{S}_4\times {\Sigma }_3$, we find a class of $Ad{S}_4\times S^3$ and $Ad{S}_4\times H^3$ solutions with four supercharges, corresponding to $N=1$ SCFTs in three dimensions. When the two $SU(2)$ gauge couplings are equal, only $Ad{S}_4\times H^3$ are possible. The uplifted solutions for equal $SU(2)$ gauge couplings to eleven dimensions are also given.

arXiv comment29 pages, 5 figures, references added, some results refined, typos and errors corrected

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Cited by in corpus (11)

• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• Revisiting the classifications of 6d SCFTs and LSTs
• BPS objects in D=7 supergravity and their M-theory origin
• Supersymmetric $Ad{S}_5$ black holes and strings from 5D $N=4$ gauged supergravity
• Five-branes wrapped on topological disks from 7D N=2 gauged supergravity
• Supersymmetric solutions from matter-coupled 7D N=2 gauged supergravity
• Twisted compactifications of 6D field theories from maximal 7D gauged supergravity
• Twisted compactification of N=2 5D SCFTs to three and two dimensions from F(4) gauged supergravity
• Two-dimensional SCFTs from matter-coupled 7D N=2 gauged supergravity
• Supersymmetric AdS4 black holes from matter-coupled N=3,4 gauged supergravities
• Wrapped D4-branes from maximal 6D gauged supergravity