PROPAGATION OF SINGULARITIES ON AdS SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue J.Inst.Math.Jussieu Année : 2022

PROPAGATION OF SINGULARITIES ON AdS SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION

Oran Gannot
  • Fonction : Auteur
Michał Wrochna
  • Fonction : Auteur

Résumé

We consider the Klein–Gordon equation on asymptotically anti-de-Sitter spacetimes subject to Neumann or Robin (or Dirichlet) boundary conditions and prove propagation of singularities along generalized broken bicharacteristics. The result is formulated in terms of conormal regularity relative to a twisted Sobolev space. We use this to show the uniqueness, modulo regularizing terms, of parametrices with prescribed $\text{b}$ -wavefront set. Furthermore, in the context of quantum fields, we show a similar result for two-point functions satisfying a holographic Hadamard condition on the $\text{b}$ -wavefront set.

Dates et versions

hal-01975027 , version 1 (09-01-2019)

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Citer

Oran Gannot, Michał Wrochna. PROPAGATION OF SINGULARITIES ON AdS SPACETIMES FOR GENERAL BOUNDARY CONDITIONS AND THE HOLOGRAPHIC HADAMARD CONDITION. J.Inst.Math.Jussieu, 2022, 21 (1), pp.67-127. ⟨10.1017/S147474802000002X⟩. ⟨hal-01975027⟩
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