Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories

We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is ${\mathrm{AdS}}_6\times {\mathrm{S}}^2$ warped over a Riemann surface. Families of solutions are labeled by an arbitrary number $L\ge 3$ 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 nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.

Figure 1

Fig. 1 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. 1 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 $\mathrm{\Sigma }$ with boundary $\partial \mathrm{\Sigma }=\mathbb{R}$. Zeros of the function $\lambda$ are at the points $s_n$ and poles at ${\overline{s}}_n$, with $n=1,\dots ,L-2$ and $\mathrm{Im}(s_n)>0$. The differentials ${\partial }_w{\mathcal{A}}_{\pm }$ have poles at the points $r_{\ell }\in \mathbb{R}$, with $\ell =1,\dots ,L$.