Existence of ghost-eliminating constraints in multivielbein theory

We perform a Hamiltonian constraint analysis of the multivielbein theory proposed in arXiv:1804.09723. The analysis shows that the secondary constraints have the correct form to constrain the dynamical variables, thereby eliminating the problematic ghost modes that generally plague theories of interacting spin-2 fields. Under mild restrictions on the solution space, we also identify the tertiary constraints and show that these eliminate the canonical momenta associated with the ghost modes. Our analysis confirms that the theory with $N$ interacting vielbeins propagates $2+5(N-1)$ modes, corresponding to a nonlinear theory of one massless and $N-1$ massive spin-2 fields free of the Boulware-Deser ghost instabilities.