Symmetry transformation of subregion bulk representations

TL;DR

This paper explores how boundary representations in AdS/CFT transform under bulk isometries, revealing their conformal transformation correspondence and implications for quantum error correction in holography.

Contribution

It demonstrates that boundary representations of AdS-Rindler wedges transform via conformal maps induced by bulk isometries, linking bulk symmetries to boundary transformations.

Findings

Boundary representations map to each other through conformal transformations.

Bulk isometries induce boundary conformal transformations.

Implications for the understanding of AdS/CFT and quantum error correction.

Abstract

Different AdS-Rindler wedges can be mapped to each other using bulk isometries. In this paper we address how the boundary representations corresponding to the AdS-Rindler wedges transform under such isometries. We show that when a bulk wedge is mapped to another using a bulk isometry, their boundary representations are mapped by the conformal transformation corresponding to the isometry. We comment on the import of this result on the relation between AdS/CFT and quantum error correction.