Understanding anti-de Sitter/conformal field theory (AdS/CFT) correspondence is of paramount importance to study quantum gravity. In this regard, the fundamental question is how the states and operators in the bulk gravity theory are reconstructed from the states and operators in the lower dimensional theory without gravity. If we can understand this bulk reconstruction, we can also explain how the bulk gravity theory emerges from the lower dimensional theory.

In the present study, we show that the bulk reconstruction in the AdS/CFT correspondence, contrary to the popular belief in the field, is rather simple and has an intuitive picture. To demonstrate this, we simplified the HKLL (Hamilton, Kabat, Lifschytz, and Lowe) bulk reconstruction formula. This can be understood as a direct consequence of the time evolution using the equations of motion of the free light-like propagating theory. This picture is completely different from what was believed in AdS/CFT correspondence.

In particular, we explicitly constructed the wave packets in the bulk theory from the CFT primary operators. This was done as follows. We first demonstrated that the bulk local operator can be represented by a linear combination of these wave packets at the same spacetime point but moving in different directions. Further, we discuss the causality and duality constraints, showing that our picture is the only consistent approach. This enables us to study the bulk spacetime from CFT as the wave packets probe bulk spacetime. In effect, in our approach, CFT is an explicit realization of the theory of quantum gravity.

Also, the BDHM (Banks, Douglas, Horowitz, and Matinec) relation, which identifies the bulk local operators on the boundary as the CFT primary fields, is important for the bulk reconstruction. Under the assumption of the BDHM relation, the present bulk reconstruction approach has potential applications in the asymptotic AdS spacetime, a non-trivial state with the bulk semi-classical description. Also, it is consistent with the Gao–Wald theorem. We underscore the importance of identifying the bulk local operators corresponding to CFT operators in a subregion. This is particularly useful for understanding the quantum entanglement in the AdS/CFT. In this study, we claim that the bulk reconstruction for the single-sided black hole is only possible for the spacetime outside the stretched horizon.

An understanding of quantum gravity is necessary for our understanding of the universe. Since spacetime in quantum gravity is represented by CFT in AdS/CFT, this research is fundamental to an enhanced understanding of quantum gravity.