Holographic duals of 6d RG flows

A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer N , an ADE group G, and two nilpotent elements μ$_{L,R}$ 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 = SU(k), where AdS$_{7}$ duals exist in IIA. We work with a seven-dimensional gauged supergravity, consisting of the gravity multiplet and two 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.