An algebraic bootstrap for dimensionally reduced quantum gravity Original Research Article

Cylindrical gravitational waves of Einstein gravity are described by an integrable system (Ernst system) whose quantization is a long standing problem. We propose to bootstrap the quantum theory along the following lines: the quantum theory is described in terms of matrix elements, e.g., of the metric operator between spectral-transformed multi-vielbein configurations. These matrix elements are computed exactly as solutions of a recursive system of functional equations, which in turn is derived from an underlying quadratic algebra. The Poisson algebra emerging in its classical limit links the spectral-transformed vielbein and the nonlocal conserved charges and can be derived from first principles within the Ernst system.