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Ghosts of Critical Gravity · Around

2011

Ghosts of Critical Gravity

Porrati, Massimo, Roberts, Matthew M.

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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.

Built on

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Original
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Then

D. Anninos, W. Li, M. Padi, W. Song, A. Strominger, “Warped AdS(3) Black Holes,” JHEP 0903
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D. Anninos, M. Esole, M. Guica, “Stability of warped AdS(3) vacua of topologically massive gravity,” JHEP 0910
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D. Grumiller, I. Sachs, “AdS (3) / LCFT (2) → \rightarrow Correlators in Cosmological Topologically Massive Gravity,” JHEP 1003
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D. Grumiller, N. Johansson, “Gravity duals for logarithmic conformal field theories,” J. Phys. Conf. Ser. 222

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S. Deser, H. Liu, H. Lu, C. N. Pope, T. C. Sisman, B. Tekin, “Critical Points of D-Dimensional Extended Gravities,” [arXiv:1101.4009 [hep-th]]

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M. Alishahiha, R. Fareghbal, “D-Dimensional Log Gravity,” [arXiv:1101.5891 [hep-th]]

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E. A. Bergshoeff, O. Hohm, J. Rosseel, P. K. Townsend, “Modes of Log Gravity,” [arXiv:1102.4091 [hep-th]]

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T. C. Sisman, I. Gullu, B. Tekin, “All unitary cubic curvature gravities in D dimensions,” [arXiv:1103.2307 [hep-th]]

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