Unitarity problems in 3D 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 perturbative 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 gravityoriginally 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.

On-shell versus off-shell equivalence in 3D gravity

“…This result shows that positivity of both c + and c − is equivalent to ±λ ∓ > 0, as claimed in subsection 3.3. It also agrees with [2] but differs from the result of [6], which is based on a quadratic action that is inequivalent to the quadratic approximation to the nonlinear MMG action.…”

“…It is therefore tempting to suppose that the quadratic action of linearized MMG must be equivalent to the quadratic action of linearized TMG. This was the premise of [6], which led to the conclusion that the known unitarity problems of TMG persist in MMG. We show here that this reasoning is mistaken because the quadratic action of linearized MMG is inequivalent to the quadratic action of TMG.…”

Exotic massive 3D gravities from truncation

“…It is desirable to study the physical properties of the extended EMG model (4.19) that we constructed in this paper further. For instance, it would be interesting to study its matter couplings [15,24] as well as its unitary extensions [23], which is hard to achieve in such models [25]. For the EMG [15], the existence of asymptotically AdS solutions obeying different boundary conditions was found in [26,27].…”

Instability of BTZ black holes in parity-even massive gravity

“…We didn't study the quasinormal frequencies of the solutions at the critical point at which Logarithmic modes are new solutions to the equations. This has been studied from different point of views in various cases in [28,29,34,35].…”