HEP Theory Journal Club

Bulk Reconstruction as Universal Approximate Subspace Error Correction

Matt Hodel

McGill

We review recent work by Hayden and Penington [arxiv:1807.06041] in which entanglement wedge reconstruction in AdS/CFT is studied away from the limit G_{N → 0 (or in gauge theory language, away from the 't Hooft large-N limit). Previous treatments of the quantum error correcting properties of AdS/CFT have worked exclusively in this semiclassical regime with a fixed background spacetime geometry, correctly interpreting the holographic dictionary in this case as an exact quantum error correcting code (QECC). It is shown that once 1/N effects are included this QECC necessarily becomes approximate. Moreover, in cases where the entanglement wedge includes black hole microstates, a lower bound can be derived for the code's error: it is nonperturbative (i.e. vanishes to all orders in the 1/N expansion) but nevertheless its absence would lead to contradictions with well-known properties of the AdS/CFT correspondence - namely, subregion-subregion duality between boundary and bulk. If time allows, connections to state dependence and the Papadodimas-Raju proposal for the black hole interior will be discussed.}