Bulk reconstruction and Bogoliubov transformations in AdS$_2$

Authors: Parijat Dey and Nirmalya Kajuri Preprint number: UUITP-27/21 Abstract: In the bulk reconstruction program, one constructs boundary representations of bulk fields. However, the boundary representations derived in global and AdS-Rindler coordinates appear to be inequivalent as the AdS-Rindler smearing function is known to diverge in dimensions greater than two. This is an apparent paradox. We investigate the relation between the two representations for AdS$_2$. 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.