Warped \(\mathrm{AdS}_{6} \times S^2 \) in type IIB supergravity. II: Global solutions and five-brane webs

DOI10.1007/JHEP05(2017)131zbMATH Open1380.83282arXiv1703.08186OpenAlexW2617497173MaRDI QIDQ683033

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Publication date: 5 February 2018

Published in: (Search for Journal in Brave)

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 $Ad{S}_{6}imes{S}^2$ warped over a two-dimensional Riemann surface $Sigma$. In earlier work, the general local solutions were expressed in terms of two locally holomorphic functions $mathcal{A}_{p}m$ 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 $mathcal{A}_{p}m$ for arbitrary $Sigma$. Global solutions exist only when $Sigma$ has a non-empty boundary $partialSigma$. The differentials $partialmathcal{A}_{p}m$ are allowed to have poles only on $partialSigma$ 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.

Full work available at URL: https://arxiv.org/abs/1703.08186

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