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 \( \frac{1}{4{G}_N} \); 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.

我们讨论了二维全息共形场理论中的一参数状态族，该状态参量是通过对双体几何中的双曲切片族的有效理论的欧几里德路径积分构造而成的。所讨论的有效理论是CFT在\（T \ overline {T} \）变形下流动，这将边界CF​​T朝着整体时间反射对称切片“折叠”。我们建议在CFT中这些新颖的欧氏路径积分状态可以解释为连续张量网络（CTN）状态。我们认为，这些CTN状态满足边界间隔的纠缠熵上的Ryu-Takayanagi式最小面积上限，系数等于\（\ frac {1} {4 {G} _N} \）; 对应于体时反射对称片的CTN使该界限饱和。我们还认为，CFT的原始状态可以写为此类CTN状态的叠加，相应的波函数为体Hartle-Hawking波函数。