Building tensor networks for holographic states

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 TT 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 14GN; the CTN corresponding to the bulk time-reflection symmetric slice saturates this bound. We also argue that the original state of the CFT can be written as a superposition of such CTN states, with the corresponding wavefunction being the bulk Hartle-Hawking wavefunction.

Automated summary

In this paper, we discuss a novel family of Euclidean path integral states in two-dimensional holographic conformal field theories, which can be interpreted as continuous tensor network (CTN) states. These CTN states satisfy a Ryu-Takayanagi-like minimal area upper bound on entanglement entropies, with a coefficient of 14GN. The original state of the CFT can be expressed as a superposition of such CTN states, with the corresponding wavefunction being the bulk Hartle-Hawking wavefunction.