  We review the results of arXiv:hep-th/0703190, on brane induced gravity (BIG)
in 6D. Among a large diversity of regulated codimension-2 branes, we find that
for near-critical tensions branes live inside very deep throats which
efficiently compactify the angular dimension. In there, 4D gravity first
changes to 5D, and only later to 6D. The crossover from 4D to 5D is independent
of the tension, but the crossover from 5D to 6D is not. This shows how the
vacuum energy problem manifests in BIG: instead of tuning vacuum energy to
adjust the 4D curvature, generically one must tune it to get the desired
crossover scales and the hierarchy between the scales governing the 4D \to 5D
\to 6D transitions. In the near-critical limit, linearized perturbation theory
remains under control below the crossover scale, and we find that linearized
gravity around the vacuum looks like a scalar-tensor theory.
