Unitarity Problems in 3$D$ Gravity Theories

Abstract

We revisit the problem of the bulk-boundary unitarity clash in 2 + 1 dimensional gravity theories, which has been an obstacle in providing a viable dual two-dimensional conformal field theory for bulk gravity in anti-de Sitter (AdS) spacetime. Chiral gravity, which is a particular limit of cosmological topologically massive gravity (TMG), suffers from pertur- bative log-modes with negative energies inducing a non-unitary logarithmic boundary field theory. We show here that any f(R) extension of TMG does not improve the situation. We also study the perturbative modes in the metric formulation of minimal massive gravity- originally constructed in a first-order formulation-and find that the massive mode has again negative energy except in the chiral limit. We comment on this issue and also discuss a possible solution to the problem of negative energy modes. In any of these theories, the infinitesimal dangerous deformations might not be integrable to full solutions; this suggests a linearization instability of AdS spacetime in the direction of the perturbative log-modes.

arXiv comment15 pages, matches the Physics. Rev. D version

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Cited by in corpus (11)

• On Complexity Growth in Minimal Massive 3D Gravity
• Causality in 3D Massive Gravity Theories
• Bachian Gravity in Three Dimensions
• Linearization Instability for Generic Gravity in AdS
• Homogeneous Solutions of Minimal Massive 3D Gravity
• Nonlocal Massive Gravity from Einstein Gravity
• On-shell versus Off-shell Equivalence in 3D Gravity
• Exotic Massive Gravity: Causality and a Birkhoff-like Theorem
• Instability of BTZ black holes in parity-even massive gravity
• Solutions with pure radiation and gyratons in 3D massive gravity theories
• Aspects of three-dimensional higher-curvature gravities