We obtain the complete local solutions with 16 supersymmetries to Type IIB supergravity on a space-time of the form AdS 2 × S 6 warped over a Riemann surface Σ in terms of two locally holmorphic functions on Σ. We construct the general Ansatz for the bosonic supergravity fields and supersymmetry generators compatible with the SO(2, 1) ⊕ SO(7) isometry algebra of space-time, which extends to the corresponding real form of the exceptional Lie superalgebra F (4). We reduce the BPS equations to this Ansatz, obtain their general local solutions, and show that these local solutions solve the full Type IIB supergravity field equations and Bianchi identities. We contrast the AdS 2 ×S 6 solution with the closely related AdS 6 × S 2 case and present our results for both in parallel. Finally, we present a preliminary analysis of positivity and regularity conditions for AdS 2 × S 6 , but postpone the construction of globally regular solutions to a subsequent paper.

We investigate half-BPS Type IIB supergravity solutions with spacetime geometry AdS 2 × S 6 warped over a Riemann surface Σ. The general local solution was obtained in earlier work in terms of two holomorphic functions A ± on Σ. In the first part of this paper we seek global solutions corresponding to the near-horizon behavior of (p, q)string junctions. We identify the type of singularity in A ± needed at the boundary of Σ to match the solutions locally onto the classic (p, q)-string solution. We construct solutions with multiple (p, q)-strings, but the existence of geodesically complete solutions remains unsettled. In a second part we construct multi-parameter families of non-compact globally regular and geodesically complete solutions with asymptotic regions and an AdS 2 throat which caps off smoothly.

We investigate the existence of solutions with 16 supersymmetries to Type IIB supergravity on a spacetime of the form AdS2× S5× S1 warped over a two-dimensional Riemann surface Σ. The existence of the Lie superalgebra SU(1, 1|4) ⊂ PSU(2, 2|4), whose maximal bosonic subalgebra is SO(1, 2)⊕SO(6)⊕SO(2), motivates the search for half-BPS solutions with this isometry that are asymptotic to AdS5×S5. We reduce the BPS equations to the Ansatz for the bosonic fields and supersymmetry generators compatible with these symmetries, then show that the only non-trivial solution is the maximally supersymmetric solution AdS5× S5. We argue that this implies that no solutions exist for fully back-reacted D7 probe or D7/D3 intersecting branes whose near-horizon limit is of the form AdS2× S5× S1× Σ.