Warped AdS6 × S 2 in Type IIB supergravity II: global solutions and five-brane webs

• Main Authors: Eric D’Hoker, Michael Gutperle, Christoph F. Uhlemann
• Format: Article
• Language: English
• Published: SpringerOpen 2017-05-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Gauge-gravity correspondence; p-branes; Superstring Vacua
• Online Access: http://link.springer.com/article/10.1007/JHEP05(2017)131

Abstract 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 × 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 $$ \mathcal{A} $$ ± 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 $$ \mathcal{A} $$ ± for arbitrary Σ. Global solutions exist only when Σ has a non-empty boundary ∂Σ. The differentials ∂ A $$ \mathcal{A} $$ ± 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.