Quantized Einstein–Rosen waves, AdS2, 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 AdS2. Thornʹs C-energy is one of the sl(2,R) generators, the reconstruction from the (timelike) symmetry axis is the CFT1 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 AdS2 conformal invariance remains intact.