We investigate the existence of solutions with 16 residual supersymmetries to Type IIB supergravity on a space-time of the form AdS 6 ×S 2 warped over a two-dimensional Riemann surface Σ. The SO(2, 5) × SO(3) isometry extends to invariance under the exceptional Lie superalgebra F (4). In the present paper, we construct the general Ansatz compatible with these symmetries, derive the corresponding reduced BPS equations, and obtain their complete local solution in terms of two locally holomorphic functions A ± on Σ, subject to certain positivity and regularity conditions. Globally, (A + , A − ) are allowed to be multiple-valued on Σ and be holomorphic sections of a holomorphic bundle over Σ with structure group contained in SU(1, 1) × C. Globally regular solutions are expected to provide the near-horizon geometry of (p, q) 5-brane and 7-brane webs which are holographic duals to five-dimensional conformal field theories. A preliminary analysis of the positivity and regularity conditions will be presented here, leaving the construction of globally regular solutions to a subsequent paper.

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 × S 2 warped over a two-dimensional Riemann surface Σ. In earlier work, the general local solutions were expressed in terms of two locally holomorphic functions A ± on Σ and global solutions were sketched when Σ 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 Σ. Global solutions exist only when Σ has a non-empty boundary ∂Σ. The differentials ∂A ± are allowed to have poles only on ∂Σ 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.

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 × S 2 warped over a Riemann surface Σ by allowing the supergravity fields to have non-trivial SL(2, R) monodromy at isolated punctures on Σ. We obtain explicit solutions for the case where Σ is a disc, and the monodromy generators are parabolic elements of SL(2, R) physically corresponding to the monodromy allowed in Type IIB string theory. On the boundary of Σ 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 Σ, the solutions are everywhere regular, except at the punctures where SL(2, 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.

Dedicated to John H. Schwarz on the occasion of his seventy fifth birthday.We construct global solutions to Type IIB supergravity with 16 residual supersymmetries whose space-time is AdS6 × S 2 warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L ≥ 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.