It is my understanding that in string theory, loop quantum gravity, the 'asymptotic safety' approach, and in semiclassical quantum gravity, local Poincare symmetry is exact. But there are things like DSR (does the D stand for Deformed, or Doubly? I've heard people say it either way), which while not a quantum theory of gravity, do try to have poincare invariance in the low energy limit but have terms on the order of the planck energy which violate poincare symmetry. First, is this understanding correct? (are there any 'overview' papers which mention poincare symmetry explicitly which I could refer to?) And second, can anyone list some examples of current mainstream approaches to quantum gravity that DO break local poincare symmetry? I am not aware of any. If these approaches do exist, since the poincare group representations are usually used to identify particles in field theory, how do the theories deal with this now missing piece? Do they end up with anyons in addition to fermions and bosons?