Quantized Einstein-Rosen waves, AdS_2, and spontaneous symmetry breaking
  4D cylindrical gravitational waves with aligned polarizations (Einstein-Rosen waves) are shown to be described by a weight 1/2 massive free field on the double cover of AdS_2. Thorn's C-energy is one of the sl(2,R) generators, the reconstruction from the (timelike) symmetry axis is the CFT_1 holography. Classically the phase space is also invariant under a O(1,1) group action on the metric coefficients that is a remnant of the original 4D diffeomorphism invariance. In the quantum theory this symmetry is found to be spontaneously broken while the AdS_2 conformal invariance remains intact. 
M. Niedermaier