  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.
