The structure of MERA has an interesting interpretation in light of the AdS/CFT correspondence. I'm not remotely qualified to lecture on this, so we can collectively discuss how interpreting the MERA tensor network as a spatial slice of AdS allows one to recover Ryu & Takayanagi holographic calculation of the entanglement entropy. We can then discuss Qi's formulation of MERA which provides a unitary relation between a gapless system in (d+1)-dimensions and a gapped system in AdS, and perhaps the black hole geometry realized at finite temperature.

 

Ryu & Takayanagi:

        http://arXiv.org/abs/hep-th/0603001

 

B Swingle:

        http://arxiv.org/abs/1209.3304

        http://arxiv.org/abs/0905.1317v1

 

XL Qi:

        http://arxiv.org/abs/1309.6282v1