Gravity cutoff in theories with large discrete symmetries.

We set an upper bound on the gravitational cutoff in theories with exact quantum numbers of large N periodicity, such as Z(N) discrete symmetries. The bound stems from black hole physics. It is similar to the bound appearing in theories with N particle species, though a priori, a large discrete symmetry does not imply a large number of species. Thus, there emerges a potentially wide class of new theories that address the hierarchy problem by lowering the gravitational cutoff due to the existence of large Z(10(32))-type symmetries.

Non-Pauli-Fierz massive gravitons.

We study general Lorentz invariant theories of massive gravitons. We show that, contrary to the standard lore, there exist consistent theories where the graviton mass term violates Pauli-Fierz structure. For theories where the graviton is a resonance, this does not imply the existence of a scalar ghost if the deviation from a Pauli-Fierz structure becomes sufficiently small at high energies. These types of mass terms are required by any consistent realization of the Dvali-Gabadadze-Porrati model in higher dimension.

Cascading gravity: extending the Dvali-Gabadadze-Porrati model to higher dimension.

We present a generalization of the Dvali-Gabadadze-Porrati scenario to higher codimensions which, unlike previous attempts, is free of ghost instabilities. The 4D propagator is made regular by embedding our visible 3-brane within a 4-brane, each with their own induced gravity terms, in a flat 6D bulk. The model is ghost-free if the tension on the 3-brane is larger than a certain critical value, while the induced metric remains flat. The gravitational force law "cascades" from a 6D behavior at the largest distances followed by a 5D and finally a 4D regime at the shortest scales.