Existence of ghost-eliminating constraints in multivielbein theory

TL;DR

The paper performs a comprehensive Hamiltonian constraint analysis of the multivielbein theory with \\mathcal{N} interacting vielbeins. By deriving the full set of primary, secondary, tertiary, and higher constraints and examining their time evolution, it demonstrates that ghost degrees of freedom can be eliminated under a controlled Ansatz and constraint structure. The analysis shows the theory propagates exactly \\text{2 + 5(}\\mathcal{N}-1) } modes, corresponding to one massless and \\mathcal{N}-1$ massive spin-2 fields, with a constraint algebra that mirrors diagonal diffeomorphism and Lorentz invariance. This establishes the nonlinearly ghost-free nature of the multivielbein model (at least within the equal-boost sector and under the identified constraints), highlighting its potential as a consistent nonlinear theory of multiple interacting spin-2 fields with Boulware–Deser ghost absent in the physical spectrum.

Abstract

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.