Symmetries from Locality. II. Gravitation and Lorentz Boosts
  It is known that local, Lorentz invariant, unitary theories involving
particles with spin 1 demand that the matter sector they couple to are
organized by internal physical symmetries and the associated charge
conservation, while spin 3/2 demands supersymmetry. However, the introduction
of a spin 2 graviton does not obviously demand new symmetries of the matter
sector (although it does demand a universal coupling). In this work we relax
the assumption of Lorentz boost symmetry, while maintaining a basic notion of
locality that there is no instantaneous signaling at a distance. This extends
and complements our accompanying work in Part 1 on related issues for spin 1
particles in electromagnetism. In order to avoid potential problems with
longitudinal modes of the graviton, we choose to project them out, leaving only
two degrees of freedom. We study large classes of theories that a priori may
violate Lorentz boost invariance. By requiring the tree-level exchange action
be local, we find that consistency demands that the Lorentz boost symmetry must
be satisfied by the graviton and the matter sector, and in turn we recover
general relativity at this order of analysis.
