IIB Duals of D=3 N=4 Circular Quivers

TL;DR

The work constructs type-IIB AdS$_4$ backgrounds dual to IR fixed points of 3d ${\cal N}=4$ circular-quiver gauge theories, encoded by the data $(\rho,\hat{\rho},L)$, and shows that in the large-$L$ limit these solutions reproduce M-theory on $AdS^4\times S^7/(\mathbb{Z}_k\times\mathbb{Z}_{\hat{k}})$ while resolving the singularities via five-brane throats. It provides a precise holographic dictionary matching the IR quiver data to the supergravity charges, and demonstrates that the circular-quiver data naturally map to an annulus-based harmonic-function construction, generalizing prior linear-quiver results. A novel outcome is a proposed orbifold equivalence under $SL(2,\mathbb{Q})$, with quantitative support from exact $S^3$ partition function comparisons, suggesting deep connections between distinct ${\cal N}=4$ SCFTs in the large-$N$ limit. The paper also explores limiting geometries (pinched annulus and smeared branes) to connect to wormbrane pictures and M2-brane orbifolds, and discusses $(p,q)$-brane generalizations and their implications for dualities and free energies.

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.

Figures (16)

• Figure 1: A linear quiver with $\hat{k}-1$ gauge-group factors $U(N_1)\times U(N_2)\times\cdots$. The red boxes indicate the numbers of hypermultiplets in the fundamental representation of each gauge-group factor.
• Figure 2: A circular quiver with $\hat{k}$ gauge-group factors. The $U(N_i)$ theories interact via bifundamental hypermultiplets (the blue lines) which form a circular chain, as opposed to the linear chain of figure 1.
• Figure 3: Brane realization of linear quivers
• Figure 4: Pushing all D5-branes to the right of all NS5-branes makes it easy to read the linking numbers, as the net number of D3-branes ending on each five-brane. In this example $\rho = (3,2, \cdots 2)$ and $\hat{\rho} = (4, 2, \cdots 1)$.
• Figure 5: Brane realization of circular quivers. To attribute linking numbers to the five-branes we cut open the $k$-th stack of D3 branes, and place the $k$-th D5 stack at the left-most end.