Holographic duals of 6d RG flows

Abstract

A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer $N$, an ADE group $G$, and two nilpotent elements ${\mu }_{\mathrm{L},\mathrm{R}}$ in $G$. Nilpotent elements have a natural partial ordering, which has been conjectured to coincide with the hierarchy of renormalization-group flows among the SCFTs. In this paper we test this conjecture for $G=\mathrm{SU}(k)$, where AdS${}_7$ duals exist in IIA. We work with a seven-dimensional gauged supergravity, consisting of the gravity multiplet and two $\mathrm{SU}(k)$ non-Abelian vector multiplets. We show that this theory has many supersymmetric AdS${}_7$ vacua, determined by two nilpotent elements, which are naturally interpreted as IIA AdS${}_7$ solutions. The BPS equations for domain walls connecting two such vacua can be solved analytically, up to a Nahm equation with certain boundary conditions. The latter admit a solution connecting two vacua if and only if the corresponding nilpotent elements are related by the natural partial ordering, in agreement with the field theory conjecture.

arXiv comment33 pages, 2 figures

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Cited by in corpus (13)

• On AdS${}_7$ stability
• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Supersymmetric AdS${}_7$ and AdS${}_6$ vacua and their consistent truncations with vector multiplets
• Charges and holography in 6d (1,0) theories
• Consistent truncations of supergravity and $\frac{1}{2}$-BPS RG flows in $4d$ SCFTs
• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions
• Supersymmetric domain walls in 7D maximal gauged supergravity
• Holographic RG flows and Janus solutions from matter-coupled N=4 gauged supergravity
• Two-dimensional SCFTs from matter-coupled 7D N=2 gauged supergravity
• Isomorphisms of 4d N=2 SCFTs from 6d
• Mink${}_4\times S^2$ Solutions of 10 and 11 Dimensional Supergravity
• Non-supersymmetric AdS${}_6$ and the swampland
• On SUSY-breaking Moduli Spaces of AdS${}_7$ Vacua and 6D SCFTs