Static patch solipsism: conformal symmetry of the de Sitter worldline. (English) Zbl 1253.83014
This paper is concerned with the holographic description of the static patch of de Sitter (dS) space-time, focussing particularly on the retarded Green’s function of scalar fields and gravitons seen by a static observer.
The central idea is to use the conformal relationship between dS times the real line and three-dimensional anti-de Sitter (adS) space-time times a sphere. Quasi-normal mode frequencies, corresponding to poles in the Green’s function, come in two families in general and two \(\mathrm{SL}(2,\mathbb{R})\) algebras act as ladder operators on these families. This “hidden” \(\mathrm{SL}(2,\mathbb{R})\times \mathrm{SL}(2,\mathbb{R})\) symmetry is explored in some detail.
The title of this paper is somewhat intriguing: what is meant by “solipsism”? In simple terms, it is a type of gauge-fixing, whereby a single static observer is considered.
The central idea is to use the conformal relationship between dS times the real line and three-dimensional anti-de Sitter (adS) space-time times a sphere. Quasi-normal mode frequencies, corresponding to poles in the Green’s function, come in two families in general and two \(\mathrm{SL}(2,\mathbb{R})\) algebras act as ladder operators on these families. This “hidden” \(\mathrm{SL}(2,\mathbb{R})\times \mathrm{SL}(2,\mathbb{R})\) symmetry is explored in some detail.
The title of this paper is somewhat intriguing: what is meant by “solipsism”? In simple terms, it is a type of gauge-fixing, whereby a single static observer is considered.
Reviewer: Elizabeth Winstanley (Sheffield)
MSC:
| 83C45 | Quantization of the gravitational field |
| 53Z05 | Applications of differential geometry to physics |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81S10 | Geometry and quantization, symplectic methods |
