Holographic Duals of D=3 N=4 Superconformal Field Theories

TL;DR

The work constructs explicit warpings of Type-IIB supergravity, yielding AdS4×K backgrounds that holographically dualize a large family of 3D ${\mathcal N}=4$ SCFTs labeled by partitions $(\rho,\hat{\rho})$ of $N$, identified as IR fixed points of mirror-symmetric quivers $T^{\rho}_{\hat{\rho}}(SU(N))$ and their S-duals. The authors derive a gravitational version of the field-theory fixed-point constraint, show that the global symmetry $H_{\rho}\times H_{\hat{\rho}}$ is realized by bulk degrees of freedom on five-brane stacks, and map the gravitational data to the quiver data via the brane linking numbers, including a detailed treatment of brane charges, Page charges, and flux quantization. A key feature is the analysis of degeneration limits where AdS5×S^5 regions decouple or warp into wormhole-like connections between multiple AdS4 regions, corresponding to factorization of the quiver into subquivers connected by weak links. The results provide a concrete string-theory realization of a rich class of 3D fixed-point theories, enabling quantitative tests (e.g., partition functions on S^3) and offering insights into brane dynamics, holographic duality, and possible gravity-localization phenomena.

Abstract

We find the warped AdS_4 x K type-IIB supergravity solutions holographically dual to a large family of three dimensional \cN=4 superconformal field theories labeled by a pair (ρ,\hatρ) of partitions of N. These superconformal theories arise as renormalization group fixed points of three dimensional mirror symmetric quiver gauge theories, denoted by T^ρ_{\hat ρ}(SU(N)) and T_ρ^{\hat ρ}(SU(N)) respectively. We give a supergravity derivation of the conjectured field theory constraints that must be satisfied in order for these gauge theories to flow to a non-trivial supersymmetric fixed point in the infrared. The exotic global symmetries of these superconformal field theories are precisely realized in our explicit supergravity description.

Figures (6)

• Figure 1: A linear quiver: circles denote gauge group factors $U(N_j)$, while squares stand for hypermultiplets in the fundamental representation of the corresponding factor group. There is also one bi-fundamental hypermultiplet for each neighbouring pair of gauge group factors, denoted by a single blue line.
• Figure 2: A brane configuration with $N=6$, $\rho = (2,2,1,1)$ and $\hat{\rho} = (3,2,1)$ .
• Figure 3: On the left, the brane construction of figure 2 after moving the D5-branes in the way described in the text. On the right the quiver diagram describing the corresponding supersymmetric gauge theory.
• Figure 4: The four asymptotic regions of the solution (\ref{['hNS5D5']}): near $z\simeq \pm\infty$ the geometry asymptotes to $AdS_5 \times S^5$, while the singularities on the lower and the upper strip boundary describe stacks of NS5 branes and D5 branes. Taking $\alpha$ and $\hat{\alpha}$ to zero replaces the $AdS_5 \times S^5$ regions by smooth caps homeomorphic to $AdS_4$ times a 6-dimensional ball.
• Figure 5: The infinite strip with several singularities, corresponding to many different stacks of five-branes. The positions of these singularities along the real axis are related to the data of the dual superconformal field theory, in a way that will be detailed in section \ref{['sec:charge']}.