Warped $AdS_6\times S^2$ in Type IIB supergravity III: Global solutions with seven-branes

We extend our previous construction of global solutions to Type IIB supergravity that are invariant under the superalgebra $F(4)$ and are realized on a spacetime of the form $AdS_6 \times S^2$ warped over a Riemann surface $\Sigma$ by allowing the supergravity fields to have non-trivial $SL(2,{\mathbb R})$ monodromy at isolated punctures on $\Sigma$. We obtain explicit solutions for the case where $\Sigma$ is a disc, and the monodromy generators are parabolic elements of $SL(2,{\mathbb R})$ physically corresponding to the monodromy allowed in Type IIB string theory. On the boundary of $\Sigma$ the solutions exhibit singularities at isolated points which correspond to semi-infinite five-branes, as is familiar from the global solutions without monodromy. In the interior of $\Sigma$, the solutions are everywhere regular, except at the punctures where $SL(2,{\mathbb R})$ monodromy resides and which physically correspond to the locations of $[p,q]$ seven-branes. The solutions have a compelling physical interpretation corresponding to fully localized five-brane intersections with additional seven-branes, and provide candidate holographic duals to the five-dimensional superconformal field theories realized on such intersections.