Wave packets in AdS/CFT correspondence

In this paper, we construct a general bulk wave packet in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>AdS</a:mi><a:mo>/</a:mo><a:mi>CFT</a:mi></a:mrow></a:math> correspondence. This wave packet can be described both in bulk and conformal field theory (CFT) descriptions. Then, we compute the time evolution of the energy density of this wave-packet state on the vacuum in the CFT picture of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>AdS</c:mi><c:mn>3</c:mn></c:msub><c:mo>/</c:mo><c:msub><c:mi>CFT</c:mi><c:mn>2</c:mn></c:msub></c:math>. We find that the energy density of the wave packet is localized at two points, which means that the bulk wave packet corresponds to two light-like particle-like objects in the CFT picture. Our result implies that the entanglement wedge reconstruction given by Almheiri [Bulk locality and quantum error correction in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>AdS</e:mi><e:mo>/</e:mo><e:mi>CFT</e:mi></e:mrow></e:math>, is invalid.