Building Tensor Networks for Holographic States

Understand

We discuss a one-parameter family of states in two-dimensional holographic conformal field theories which are constructed via the Euclidean path integral of an effective theory on a family of hyperbolic slices in the dual bulk geometry.

• The effective theory in question is the CFT flowed under a $T\overline{T}$ deformation, which "folds" the boundary CFT towards the bulk time-reflection symmetric slice.
• We propose that these novel Euclidean path integral states in the CFT can be interpreted as continuous tensor network (CTN) states.
• We argue that these CTN states satisfy a Ryu-Takayanagi-like minimal area upper bound on the entanglement entropies of boundary intervals, with the coefficient being equal to $\frac{1}{4G_N}$; the CTN corresponding to the bulk time-reflection symmetric slice saturates this bound.