Interacting spin-2 fields in three dimensions

Abstract

Using the frame formulation of multi-gravity in three dimensions, we show that demanding the presence of secondary constraints which remove the Boulware-Deser ghosts restricts the possible interaction terms of the theory and identifies invertible frame field combinations whose effective metric may consistently couple to matter. The resulting ghost-free theories can be represented by theory graphs which are trees. In the case of three frame fields, we explicitly show that the requirement of positive masses and energies for the bulk spin-2 modes in AdS${}_3$ is consistent with a positive central charge for the putative dual CFT${}_2$.

26 pages, 3 figures, v2: minor changes, matches published version

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Cited by in corpus (19)

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• Spontaneously Broken 3d Hietarinta/Maxwell Chern-Simons Theory and Minimal Massive Gravity
• Einstein Gravity, Massive Gravity, Multi-Gravity and Nonlinear Realizations
• New Kinetic Terms for Massive Gravity and Multi-gravity: A No-Go in Vielbein Form
• Exotic massive 3D gravities from truncation
• On asymptotic charges in 3D gravity
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Interactions of multiple spin-2 fields beyond pairwise couplings
• Multimetric Supergravities
• Soft hairy warped black hole entropy
• Unitary Extension of Exotic Massive 3D Gravity from Bi-gravity
• On the Faddeev-Jackiw Symplectic Framework for Topologically Massive Gravity
• Gauge symmetry and constraints structure in topologically massive AdS gravity: A symplectic viewpoint
• Mass spectrum and linear perturbations of ghost-free multi-spin-2 theory
• Symplectic realization of two interacting spin-two fields in three dimensions
• Faddeev-Jackiw Hamiltonian formulation for general exotic bi-gravity
• Chern-Simons-Like Formulation of Exotic Massive 3D Gravity Models
• Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework
• Hamiltonian structure of three-dimensional gravity in Vielbein formalism