IIB Duals of D=3 N=4 Circular Quivers

Abstract

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 $(ρ,\hat ρ,L)$ subject to constraints, where $ρ$ and $\hat ρ$ 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 $(ρ,\hatρ,L)$, 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.

53 pages, 16 figures. Added several comments and some extra references on the relation of our IIB solutions to M theory. Paper to appear in JHEP