Brane induced gravity: From a no-go to a no-ghost theorem

Abstract

Numerous claims in the literature suggest that gravity induced on a higher codimensional surface violates unitarity in the weak coupling regime. However, it remained unclear, why a conserved source localized on this surface and giving rise to an induced gravity term at low energies would absorb and emit the associated ghost, given a consistent source-free theory. In this article it is shown that the appearance of the induced Einstein-Hilbert term does not threaten the unitarity of the theory. It is shown that the would-be ghost highlighted in previous works is nondynamical and therefore not associated with a state in the Hilbert space. The physics arguments behind this statement are presented in a semicovariant language, but the detailed proof is given using Dirac's constraint analysis. The Hamiltonian on the constraint surface of the linearized theory is derived and turns out to be manifestly positive definite. As a result of these investigations, brane-induced gravity goes without a ghost, opening an exciting window of opportunity for consistent deformations of gravity at the largest observable distances.