The known ghost-free multivielbein theory is the unique ghost-free theory with genuine multi-field interactions for more than two vielbeins.
Analysis of constraints and their algebra in bimetric theory
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abstract
We perform a canonical analysis of the bimetric theory in the metric formulation, computing the constraints and their algebra explicitly. In particular, we compute a secondary constraint, that has been argued to exist earlier, and show that it has the correct form to eliminate the ghost. We also identify a set of four first class constraints that generate the algebra of general covariance. The covariance algebra naturally determines a spacetime metric for the theory. However, in bimetric theory, this metric is not unique but depends on how the first class constraints are identified.
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Bimetric interactions are defined via a congruence matrix, with the square root shown as the unique power series solution and algebraic equivalence to the unconstrained vielbein formulation.
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On the Uniqueness of Ghost-Free Multi-Gravity -- II: Constraining antisymmetrised multi spin-2 interactions
The known ghost-free multivielbein theory is the unique ghost-free theory with genuine multi-field interactions for more than two vielbeins.
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Bimetric interactions based on metric congruences
Bimetric interactions are defined via a congruence matrix, with the square root shown as the unique power series solution and algebraic equivalence to the unconstrained vielbein formulation.