Quantized Einstein-Rosen waves, AdS_2, and spontaneous symmetry breaking

TL;DR

This paper demonstrates that 4D Einstein-Rosen gravitational waves can be modeled as a massive free field on AdS_2, revealing spontaneous symmetry breaking of certain classical symmetries while preserving conformal invariance in the quantum regime.

Contribution

It introduces a novel quantum description of Einstein-Rosen waves as a free field on AdS_2 and uncovers spontaneous symmetry breaking of classical O(1,1) symmetry.

Findings

Quantum symmetry is spontaneously broken.

AdS_2 conformal invariance remains unbroken.

Einstein-Rosen waves are described by a massive free field.

Abstract

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.