  Entanglement renormalization is a real-space renormalization group (RG)
transformation for quantum many-body systems. It generates the multi-scale
entanglement renormalization ansatz (MERA), a tensor network capable of
efficiently describing a large class of many-body ground states, including
those of systems at a quantum critical point or with topological order. The
MERA has also been proposed to be a discrete realization of the holographic
principle of string theory. In this paper we propose the use of symmetric
tensors as a mechanism to build a symmetry protected RG flow, and discuss two
important applications of this construction. First, we argue that symmetry
protected entanglement renormalization produces the proper structure of RG
fixed-points, namely a fixed-point for each symmetry protected phase. Second,
in the context of holography, we show that by using symmetric tensors, a global
symmetry at the boundary becomes a local symmetry in the bulk, thus explicitly
realizing in the MERA a characteristic feature of the AdS/CFT correspondence.
