Brane induced gravity: Ghosts and naturalness

Linear stability of brane induced gravity in two codimensions on a static pure tension background is investigated. The brane is regularized as a ring of finite circumference in extra space. By explicitly calculating the vacuum persistence amplitude of the corresponding quantum theory, we show that the parameter space is divided into two regions - one corresponding to a stable Minkowski vacuum on the brane and one being plagued by ghost instabilities. This analytical result affirms a recent nonlinear, but mainly numerical analysis. The main result is that the ghost is absent for a sufficiently large brane tension, in perfect agreement with a value expected from a natural effective field theory point of view. Unfortunately, the linearly stable parameter regime is either ruled out phenomenologically or becomes unstable for nontrivial cosmologies. We argue that super-critical brane backgrounds constitute the remaining window of opportunity. In the special case of a tensionless brane, we find that the ghost exists for all phenomenologically relevant values of the induced gravity scale. Regarding this case, there are contradicting results in the literature, and we are able to fully resolve this controversy by explicitly uncovering the errors made in the "no-ghost" analysis. Finally, a Hamiltonian analysis generalizes the ghost result to more than two codimensions.