Ghosts of Critical Gravity

Abstract

Recently proposed "critical" higher-derivative gravities in $Ad{S}_D$ $D>3$ 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.

v2: typos corrected and slight clarifications. 11 pages

References in corpus (9)

• Massive Gravity in Three Dimensions
• Warped AdS_3 Black Holes
• Critical Gravity in Four Dimensions
• Topologically Massive Gravity and the AdS/CFT Correspondence
• Critical Points of D-Dimensional Extended Gravities
• AdS Waves as Exact Solutions to Quadratic Gravity
• D-Dimensional Log Gravity
• Modes of Log Gravity
• Stability of warped AdS3 vacua of topologically massive gravity

Cited by in corpus (1)

• Critical gravity as van Dam-Veltman-Zakharov discontinuity in anti de Sitter space