Ghosts of Critical Gravity

Details Ghosts of Critical Gravity Ghosts of Critical Gravity

2011-04-04

arxiv.org/abs/1104.0674v2

Phys.Rev.D84:024013,2011

Physics

High Energy Physics

High Energy Physics - Theory

v2: typos corrected and slight clarifications. 11 pages

Scientific paper

10.1103/PhysRevD.84.024013

Recently proposed "critical" higher-derivative gravities in $AdS_D$ $D>3$ are expected to carry logarithmic representation of the Anti de Sitter isometry group. In this note, we quantize linear fluctuations of these critical gravities, which are known to be either identical with linear fluctuations of Einstein's gravity or else satisfy logarithmic boundary conditions at spacial infinity. We identify the scalar product uniquely defined by the symplectic structure implied by the classical action, and show that it does not posses null vectors. Instead, we show that the scalar product between any two Einstein modes vanishes, while the scalar product of an Einstein mode with a logarithmic mode is generically nonzero. This is the basic property of logarithmic representation that makes them neither unitary nor unitarizable.

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