Warped AdS6 x S2 in Type IIB supergravity II: global solutions and five-brane webs

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 AdS6 x 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 A +/- 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 A +/- for arbitrary Sigma. Global solutions exist only when F has a non-empty boundary partial derivative Sigma. The differentials partial derivative.A +/- are allowed to have poles only on DE and each pole corresponds to a semi-infinite (p, q) five-brane. The construction for the disk is carried out in detail and the conditions for the existence of global solutions are articulated for surfaces with more than one boundary and higher genus.