Holographic duals for five-dimensional superconformal quantum field theories

TL;DR

This work addresses the holographic description of five-dimensional SCFTs, which arise as UV fixed points of non-renormalizable Yang-Mills theories, by constructing explicit global Type IIB supergravity solutions with $SO(2,5)\oplus SO(3)$ symmetry on $AdS_6 \times S^2$ warped over a Riemann surface $\Sigma$. Building on local BPS solutions, the authors obtain regular global geometries parameterized by an integer $L \ge 3$ of asymptotic regions, each matching the near-horizon of a $(p,q)$ five-brane and corresponding to external legs of a five-brane web; the near-pole analysis reproduces the expected brane behavior, including charge conservation constraints. The moduli of the global solutions precisely match the external brane charges after accounting for $SL(2,\mathbb{R})$ equivalences, providing a robust gravity dual for a large class of 5D SCFTs and enabling quantitative AdS/CFT studies. This work lays the groundwork for computing entanglement entropies, free energies, spectra, and correlation functions in these theories, offering a direct probe of non-Lagrangian fixed points in five dimensions.

Abstract

We construct global solutions to Type IIB supergravity with 16 residual supersymmetries whose space-time is $AdS_6 \times S^2$ warped over a Riemann surface. Families of solutions are labeled by an arbitrary number $L\geq 3$ of asymptotic regions, in each of which the supergravity fields match those of a $(p,q)$ five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in Type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as non-trivial UV fixed points of perturbatively non-renormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.

Figures (2)

• Figure 1: Fig. \ref{['fig:weba']} shows a $(p,q)$ 5-brane web for an SU(2) Yang-Mills theory with one flavor at a generic point on the Coulomb branch. Fig. \ref{['fig:webb']} shows the counterpart of (a) for the conformal limit at the origin of the Coulomb branch. It is characterized by the $(p,q)$ charges of the external 5-branes, which give the slopes of the branes in the figure.
• Figure 2: The upper half plane $\Sigma$ with boundary $\partial \Sigma = \mathds{R}$. Zeros of the function $\lambda$ are at the points $s_n$ and poles at $\bar{s}_n$, with $n=1,\cdots, L-2$ and ${\rm Im \,} (s_n) >0$. The differentials $\partial_w \mathcal{A}_\pm$ have poles at the points $r_\ell \in \mathds{R}$ with $\ell =1, \cdots, L$.