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Interacting spin-2 fields in three dimensions
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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$_2$.
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Existence of ghost-eliminating constraints in multivielbein theory
Under an equal-boost restriction and an assumed common 3+1 slicing, multivielbein theory possesses tertiary constraints that kill the ghost momenta, supporting a 2+5(N−1) mode count.
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