\(\text{AdS}_2\) quantum gravity and string theory. (English) Zbl 0965.81097

Summary: \(\text{AdS}_2\) has an \(\text{SL}(2,\mathbb{R})\) isometry group. It is argued that in the context of quantum gravity on \(\text{AdS}_2\) this group is enlarged to the full infinite-dimensional \(1+1\) conformal group. Massive scalar fields are coupled to \(\text{AdS}_2\) gravity and shown to have associated conformal weights \(h(m)\) shifted by their mass. For integral values of h primary boundary operators are obtained as \(h\) normal derivatives of the scalar field. \(\text{AdS}_2\) string theories arise in the ‘very-near-horizon’ limit of \(S^1\)-compactified \(\text{AdS}_3\) string theories. This limit corresponds to energies far below the compactification scale. The dual conformal field theory has one null dimension and can in certain cases be described as the discrete light cone quantization of a two-dimensional deformed symmetric-product conformal field theory. Evidence is given that the \(\text{AdS}_2\) Virasoro algebra is related to the right-moving \(\text{AdS}_3\) Virasoro algebra by a topological twist which shifts the central charge to zero.


81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83C80 Analogues of general relativity in lower dimensions
83E30 String and superstring theories in gravitational theory
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