The Third Way to 3D Gravity

Abstract

Consistency of Einstein's gravitational field equation $G_{\mu \nu }\propto T_{\mu \nu }$ imposes a "conservation condition" on the $T$-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 "non-geometrical" action: one {\it 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 vs. 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.

Written for the Gravity Research Foundation essay competition 2015, received an honorable mention

References in corpus (6)

• Massive Gravity in Three Dimensions
• Minimal Massive 3D Gravity
• New massive gravity, extended
• Matter coupling in 3D "Minimal Massive Gravity"
• Minimal Massive 3D Gravity Unitarity Redux
• Yang-Mills as massive Chern-Simons theory: a third way to three-dimensional gauge theories

Cited by in corpus (25)

• Exotic Massive 3D Gravity
• Most general theory of 3d gravity: Covariant phase space, dual diffeomorphisms, and more
• Higher Derivative Supergravities in Diverse Dimensions
• Rainbow Valley of Colored (Anti) de Sitter Gravity in Three Dimensions
• Exotic massive 3D gravities from truncation
• On asymptotic charges in 3D gravity
• Bachian Gravity in Three Dimensions
• Unitarity Problems in 3$D$ Gravity Theories
• Vacua of Exotic Massive 3D Gravity
• The Third Way to Interacting $p$-form Theories
• Energy of asymptotically AdS black holes in Exotic Massive Gravity and its log-extension
• More on vacua of exotic massive 3D gravity
• The Holographic c-theorem and Infinite-dimensional Lie Algebras
• Metric formulation of the simple theory of 3d massive gravity
• On-shell versus Off-shell Equivalence in 3D Gravity
• Colourful Poincaré symmetry, gravity and particle actions
• A remarkably simple theory of 3d massive gravity
• The Third way to 3D Supersymmetric Massive Yang-Mills Theory
• A note on the third way consistent deformation of Yang-Mills theory
• A Review of Third Way Consistent Theories
• Critical points of the Exotic Massive 3D Gravity
• Chern-Simons-Like Formulation of Exotic Massive 3D Gravity Models
• Unitarity Flow in 2+1 Dimensional Massive Gravity
• Perturbative Unitarity Calls for An Action
• Canonical description of Exotic General Massive Gravity