TY - UNPB

T1 - Warped $AdS_6\times S^2$ in Type IIB supergravity II

T2 - Global solutions and five-brane webs

AU - D'Hoker, Eric

AU - Gutperle, Michael

AU - Uhlemann, Christoph F.

N1 - 58 pages, 9 figures; v2: minor corrections; v3: integration constant c_6 fixed

PY - 2017/3/23

Y1 - 2017/3/23

N2 - 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 $AdS_6 \times S^2$ warped over a two-dimensional Riemann surface $\Sigma$. In earlier work, the general local solutions were expressed in terms of two locally holomorphic functions $\mathcal A_\pm$ 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 $\mathcal A_\pm$ for arbitrary $\Sigma$. Global solutions exist only when $\Sigma$ has a non-empty boundary $\partial \Sigma$. The differentials $\partial \mathcal A_\pm$ are allowed to have poles only on $\partial \Sigma$ 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.

AB - 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 $AdS_6 \times S^2$ warped over a two-dimensional Riemann surface $\Sigma$. In earlier work, the general local solutions were expressed in terms of two locally holomorphic functions $\mathcal A_\pm$ 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 $\mathcal A_\pm$ for arbitrary $\Sigma$. Global solutions exist only when $\Sigma$ has a non-empty boundary $\partial \Sigma$. The differentials $\partial \mathcal A_\pm$ are allowed to have poles only on $\partial \Sigma$ 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.

KW - hep-th

U2 - 10.1007/JHEP05(2017)131

DO - 10.1007/JHEP05(2017)131

M3 - Preprint

BT - Warped $AdS_6\times S^2$ in Type IIB supergravity II

ER -