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

A given field theory action determines a set of field equations but other actions may yield equivalent field equations; if so they are on-shell equivalent. They may also be off-shell equivalent, being related by the elimination of auxiliary fields or by local field redefinitions, but this is not guaranteed, as we demonstrate by consideration of the linearized limit of 3D massive gravity models. Failure to appreciate this subtlety has led to incorrect conclusions in recent studies of the ``Minimal Massive Gravity'' model

The third way to 3D gravity

Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories. AJR is supported by a grant from the London Mathematical Society, and he would also like to thank the University of Groningen for hospitality during the writing of this essay.This is the author accepted manuscript. The final version is available from World Scientific via http://dx.doi.org/10.1142/S021827181544015

Unitary Truncations and Critical Gravity: a Toy Model

We investigate a higher-derivative scalar field model in a fixed d+1 dimensional AdS background as a toy model for a gravitational dual to a higher-rank logarithmic CFT. The holographic two-point correlation functions on the boundary agree with higher-rank LCFT correlation functions. For odd rank, the theory allows for a truncation to a nontrivial subspace with non-negative scalar product. We discuss possible implications for higher-derivative critical gravity theories.Comment: 23 pages. As accepted for publication in JHE

Limits of JT gravity

We construct various limits of JT gravity, including Newton-Cartan and Carrollian versions of dilaton gravity in two dimensions as well as a theory on the three-dimensional light cone. In the BF formulation our boundary conditions relate boundary connection with boundary scalar, yielding as boundary action the particle action on a group manifold or some Hamiltonian reduction thereof. After recovering in our formulation the Schwarzian for JT, we show that AdS-Carroll gravity yields a twisted warped boundary action. We comment on numerous applications and generalizations.Comment: 41 pages, 3 figures, 1 table; v2: Matches published version + Footnote 11; v3: Corrected typo in Carrollian/Galilean generalized dilaton potentia

On asymptotic charges in 3D gravity

Abstract A variant of the ADT method for the determination of gravitational charges as integrals at infinity is applied to ‘Chern–Simons-like’ theories of 3D gravity, and the result is used to find the mass and angular momentum of the BTZ black hole considered as a solution of a variety of massive 3D gravity field equations. The results agree with many obtained previously by other methods, including our own results for ‘Minimal Massive Gravity’, but they disagree with others, including recently reported results for ‘Exotic Massive Gravity’. We also find the central charges of the asymptotic conformal symmetry algebra for the generic 3D gravity model with AdS vacuum and discuss implications for black hole thermodynamics.STFC consolidated grant ST/L000385/

On asymptotic charges in 3D gravity

Abstract A variant of the ADT method for the determination of gravitational charges as integrals at infinity is applied to ‘Chern–Simons-like’ theories of 3D gravity, and the result is used to find the mass and angular momentum of the BTZ black hole considered as a solution of a variety of massive 3D gravity field equations. The results agree with many obtained previously by other methods, including our own results for ‘Minimal Massive Gravity’, but they disagree with others, including recently reported results for ‘Exotic Massive Gravity’. We also find the central charges of the asymptotic conformal symmetry algebra for the generic 3D gravity model with AdS vacuum and discuss implications for black hole thermodynamics.STFC consolidated grant ST/L000385/