I went to a talk given by Daniel Harlow at Stanford last Thursday (2016 Oct) on Emergent Locality and Gravity & Quantum Error Correction. He started from summarizing the existing attempts to solve the short distance quantum gravity problem including string theory and the attempt to quantize the metric as a local field. Then he moves on to BFSS Matrix Model + AdS/CFT correspondence. In the AdS/CFT, there are two paradoxes: one essentially concludes that all operators are trivial; the other says an operator that can’t be represented in regions A or B or C can be represented in regions A+B/B+C/C+A. How to solve the paradoxes? Quantum Error Correcting Code! Daniel finds the correspondence between a tessellation of a hyperbolic plane (representing operators I guess) and the classical solution to a quantum information problem. I haven’t fully understood his ideas yet, but I’ll try to read the following papers and update this blog post after I get some new understandings and have my questions answered!
Tensor Networks: https://arxiv.org/pdf/1503.06237.pdf
Operator, Energy, Black Hole: https://arxiv.org/pdf/1411.7041.pdf
String Theory, AdS/CFT: https://arxiv.org/abs/1409.1231