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Consider two quantum critical Hamiltonians $H$ and $\tilde{H}$ on a $d$-dimensional lattice that only differ in some region $\mathcal{R}$.
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By holographic description we mean one that extends in an additional dimension corresponding to scale or RG flow. The MERA is then a holographic description in this general sense. The term ’holography’ may also be used in a more restricted sense, where one expects the scale dimension to be locally equivalent to the other space dimensions in the bulk. By studying properties of the MERA, we expect to learn about the general structure of RG-based holographic descriptions. Examples of those are modularity LongCFT2 , and the mapping of a global symmetry at the boundary into a local symmetry in the bulk Singh
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