IIB duals of D = 3 N = 4 circular quivers

We construct the type-IIB AdS4 K supergravity solutions which are dual to the three-dimensional N = 4 superconformal field theories that arise as infrared fixed points of circular-quiver gauge theories. These superconformal field theories are labeled by a triple (ρ, ρ̂) subject to constraints, where ρ and ρ̂ are two partitions of a number N, and L is a positive integer. We show that in the limit of large L the localized five- branes in our solutions are effectively smeared, and these type-IIB solutions are dual to the near-horizon geometry of M-theory M2-branes at a ℂ⁴/(Z_k}× Z_k̂) orbifold singularity. Our IIB solutions resolve the singularity into localized five-brane throats, without breaking the conformal symmetry. The constraints satisfied by the triple (ρ, ρ̂), together with the enhanced non-abelian flavour symmetries of the superconformal field theories are precisely reproduced by the type-IIB supergravity solutions. As a bonus, we uncover a novel type of "orbifold equivalence" between different quantum field theories and provide quantitative evidence for this equivalence.