  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.
