1999/10/19 by Kostas Skenderis, Sergey N. Solodukhin · 10 citations
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Conformal map #Constant curvature #Cosmology and Gravitation Theories #Curvature #Geometry #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1016/s0370-2693(99)01467-7
published as Phys.Lett.B472:316-322,2000 · 12 pages, latex, no figures; v2: minor improvements and two references added
arxiv created 1999/10/19 · openalex publication_date 2000/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We obtain an Einstein metric of constant negative curvature given an arbitrary boundary metric in three dimensions, and a conformally flat one given an arbitrary conformally flat boundary metric in other dimensions. In order to compute the on-shell value of the gravitational action for these solutions, we propose to integrate the radial coordinate from the boundary till a critical value where the bulk volume element vanishes. The result, which is a functional of the boundary metric, provides a sector of the quantum effective action common to all conformal field theories that have a gravitational description. We verify that the so-defined boundary effective action is conformally invariant in odd (boundary) dimensions and has the correct conformal anomaly in even (boundary) dimensions. In three dimensions and for arbitrary static boundary metric the bulk metric takes a rather simple form. We explicitly carry out the computation of the corresponding effective action and find that it equals the non-local Polyakov action.