IIB Duals of D=3 N=4 Circular Quivers

We construct the type-IIB $AdS_4\times K$ supergravity solutions which are dual to the three-dimensional ${\cal N}=4$ superconformal field theories that arise as infrared fixed points of circular-quiver gauge theories. These superconformal field theories are labeled by a triple $(\rho,\hat \rho,L)$ subject to constraints, where $\rho$ and $\hat \rho$ 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 $\mathbb{C}^4/(Z_k\times Z_{\hat k})$ orbifold singularity. Our IIB solutions resolve the singularity into localized five-brane throats, without breaking the conformal symmetry. The constraints satisfied by the triple $(\rho,\hat\rho,L)$, together with the enhanced non-abelian flavour symmetries of the superconformal field theories, are precisely reproduced by the 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.