Bulk reconstruction and Bogoliubov transformations in AdS$_2$
Parijat Dey, Nirmalya Kajuri
TL;DR
This paper explores how different boundary representations of bulk fields in AdS$_2$ are related through conformal transformations and Bogoliubov transformations, enhancing understanding of bulk reconstruction in holography.
Contribution
It derives the AdS-Rindler smearing function for massive and massless fields and explicitly relates global and AdS-Rindler boundary modes via Bogoliubov transformations.
Findings
Derived the AdS-Rindler smearing function for various fields
Established the relation between boundary representations through conformal transformations
Computed the Bogoliubov transformation between global and AdS-Rindler modes
Abstract
In the bulk reconstruction program, one constructs boundary representations of bulk fields. We investigate the relation between the global/Poincare and AdS-Rindler representations for AdS. We obtain the AdS-Rindler smearing function for massive and massless fields and show that the global and AdS-Rindler boundary representations are related by conformal transformations. We also use the boundary representations of creation and annihilation operators to compute the Bogoliubov transformation relating global modes to AdS-Rindler modes for both massive and massless particles.
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