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      Liouville description of conical defects in dS\(_4\), Gibbons-Hawking entropy as modular entropy, and dS\(_3\) holography

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          Abstract

          We model the back-reaction of a massive static observer in four-dimensional de Sitter spacetime by means of a singular \(\mathbb Z_q\) quotient. The set of fixed points of the \(\mathbb Z_q\) action consists of a pair of codimension two minimal surfaces given by 2-spheres in the Euclidean geometry. The introduction of an orbifold parameter \(q>1\) permits the construction of an effective action for the bulk gravity theory with support on each of these minimal surfaces. The effective action corresponds to that of Liouville field theory on a 2-sphere with a finite vacuum expectation value of the Liouville field. The intrinsic Liouville theory description yields a thermal Cardy entropy that we reintrepret as a modular free energy at temperature \(T=q^{-1}\), whereupon the Gibbons-Hawking entropy arises as the corresponding modular entropy. We further observe that in the limit \(q\to\infty\) the four-dimensional geometry reduces to that of global dS\(_3\) spacetime, where the two original minimal surfaces can be mapped to the future and past infinities of dS\(_3\) by means of a double Wick rotation. In this limit, the Liouville theories on the two conformal boundaries become free bosons with background charge whose total central charge equals that computed using the dS\(_3\)/CFT\(_2\) correspondence.

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          Three-dimensional Einstein gravity: Dynamics of flat space

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            Notes on Quantum Liouville Theory and Quantum Gravity

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              The Geometry of the Master Equation and Topological Quantum Field Theory

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                Author and article information

                Journal
                12 June 2019
                Article
                1906.05310
                547e0cad-c3f3-4b2f-8328-82c4a0cf0241

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                21 pages, 3 figures
                hep-th gr-qc

                General relativity & Quantum cosmology,High energy & Particle physics
                General relativity & Quantum cosmology, High energy & Particle physics

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