Figure 1

All pictures are equal time snapshots of $(x^{+},x^{-},u)$-space. Top left: a network of Wilson lines, which computes CFT six-point functions. Top right: a network which computes multipoint functions. After the red tentacles are amputated, it becomes the ground state at the scale defined by the black line. The density of inputs on the network is $d\mathcal{C}\propto Kd\lambda$ so the network accepts no inputs on geodesic segments. Bottom: two amputated networks in global ${\mathrm{AdS}}_3$, which differ only by crossing symmetry, are shown in black. Crossing symmetry is implemented by shifting the feature $-00-$, which implements the projector $|0⟩⟨0|$ in computing correlation functions. The blue features—Wilson lines and projections—convert the black network into one at a coarser, uniform cutoff. Projections are necessary to accord with $d\mathcal{C}\propto Kd\lambda$ because coarse-graining eliminates degrees of freedom. The coarse-graining scheme is highly nonunique; it varies with gauge choice for $(A,\overline{A})$ and with crossing symmetry.