Saturating the unitarity bound in AdS/CFT_(AdS)
Abstract
We investigate the holographic description of CFTs defined on the cylinder and on AdS, which include an operator saturating the unitarity bound. The standard Klein-Gordon field with the corresponding mass and boundary conditions on global AdS_(d+1) and on an AdS_(d+1) geometry with AdS_d conformal boundary contains ghosts. We identify a limit in which the singleton field theory is obtained from the bulk theory with standard renormalized inner product, showing that a unitary bulk theory corresponding to an operator which saturates the unitarity bound can be formulated and that this yields a free field on the boundary. The normalizability issues found for the standard Klein-Gordon field on the geometry with AdS_d conformal boundary are avoided for the singleton theory, which offers interesting prospects for multi-layered AdS/CFT.
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Cite
@article{arxiv.1204.2054,
title = {Saturating the unitarity bound in AdS/CFT_(AdS)},
author = {Thorsten Ohl and Christoph F. Uhlemann},
journal= {arXiv preprint arXiv:1204.2054},
year = {2012}
}
Comments
7 pages, 1 figure