An Algebraic Bootstrap for Dimensionally Reduced Quantum Gravity
arXiv:hep-th/9912111 · doi:10.1016/S0550-3213(00)00207-8
Abstract
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 non-local conserved charges and can be derived from first principles within the Ernst system. Among the noteworthy features of the quantum theory are: (i) The issue of (non-)renormalizability is sidestepped and (ii) there is an apparently unavoidable ``spontaneous'' breakdown of the SL(2,R) symmetry that is a remnant of the 4D diffeomorphism invariance in the compactified dimensions.
62 pages, Latex, 2 Figures
References in corpus (1)
Cited by in corpus (8)
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