Warped $AdS_6\times S^2$ in Type IIB supergravity II: Global solutions and five-brane webs

Understand

Motivated by the construction of holographic duals to five-dimensional superconformal quantum field theories, we obtain global solutions to Type IIB supergravity invariant under the superalgebra $F(4)$ on a space-time of the form $AdS_6 \times S^2$ warped over a two-dimensional Riemann surface $\Sigma$.

• In earlier work, the general local solutions were expressed in terms of two locally holomorphic functions $\mathcal A_\pm$ on $\Sigma$ and global solutions were sketched when $\Sigma$ is a disk.
• In the present paper, the physical regularity conditions on the supergravity fields required for global solutions are implemented on $\mathcal A_\pm$ for arbitrary $\Sigma$.
• Global solutions exist only when $\Sigma$ has a non-empty boundary $\partial \Sigma$.