IIB duals of D = 3 $ \mathcal{N} = 4 $ circular quivers

Abstract

Abstract We construct the type-IIB AdS4 ⋉ K supergravity solutions which are dual to the three-dimensional $ \mathcal{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 $ \left( {\rho, \hat{\rho},L} \right) $ subject to constraints, where ρ 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}}} \left/ {{\left( {{Z_k}\times {Z_{\widehat{k}}}} \right)}} \right.} $ orbifold singularity. Our IIB solutions resolve the singularity into localized five-brane throats, without breaking the conformal symmetry. The constraints satisfied by the triple $ \left( {\rho, \hat{\rho},L} \right) $ , 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.