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 (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.