Faddeev-Jackiw Hamiltonian formulation for general exotic bi-gravity

Abstract

General exotic bi-gravity, obtained in Ozkan et al. (Phys Rev Lett 123(3):031303, 2019), is a unitary parity-preserving model which describes two interacting spin-two fields in three-dimensional spacetime. Adopting a symplectic viewpoint, we investigate the dynamical structure of general exotic bi-gravity theory. In particular, by exploiting the properties of the corresponding pre-symplectic matrix and its associated zero-modes, we explicitly derive all constraints of the theory, including the integrability conditions and scalar relationships between all the parameters and fields defining the model. Then, as an application, these scalar relationships are used for studying the anti-de Sitter background. After that, we derive the gauge transformations for the dynamical variables from the structure of the remaining zero-modes, meaning that such zero-modes are indeed the generators of the gauge symmetry of the theory. Finally, by switching off one of the four coupling constants ${\beta }_n$ and assuming the invertibility of some of the dreibeins, we find that the general exotic bi-gravity theory has two physical degrees of freedom.

arXiv commentv2: minor corrections, Matches the published version

References in corpus (26)

• The Black Hole in Three Dimensional Space Time
• Black Hole Entropy from Near-Horizon Microstates
• Massive Gravity in Three Dimensions
• Bimetric Gravity from Ghost-free Massive Gravity
• More on Massive 3D Gravity
• Instability in cosmological topologically massive gravity at the chiral point
• Black hole mass and angular momentum in topologically massive gravity
• Three dimensional loop quantum gravity: physical scalar product and spin foam models
• On Unitarity of Massive Gravity in Three Dimensions
• The Constraint Algebra of Topologically Massive AdS Gravity
• Renormalizability of Massive Gravity in Three Dimensions
• Canonical structure of topologically massive gravity with a cosmological constant
• On the Hamiltonian form of 3D massive gravity
• On the Generalized Minimal Massive Gravity
• Constraint Dynamics and Gravitons in Three Dimensions
• Chern-Simons-like Gravity Theories
• Charged Black Holes in New Massive Gravity
• Extended massive gravity in three dimensions
• Comparative Quantizations of (2+1)-Dimensional Gravity
• Holograms of Conformal Chern-Simons Gravity
• Hamiltonian analysis of BHT massive gravity
• Interacting spin-2 fields in three dimensions
• Equivalent Quantisations of (2+1)-Dimensional Gravity
• Holography of information in massive gravity using Dirac brackets
• Unitary Extension of Exotic Massive 3D Gravity from Bi-gravity
• Symplectic realization of two interacting spin-two fields in three dimensions