论文标题
Cft $ _d $来自TQFT $ _ {D+1} $通过全息张量网络和CFT $ _2 $的精确离散化
CFT$_D$ from TQFT$_{D+1}$ via Holographic Tensor Network, and Precision Discretisation of CFT$_2$
论文作者
论文摘要
我们表明，可以通过求解RG操作员的特征状态来构建$ d $尺寸（CFT $ _D $）中的保征场理论的路径综合，此后是从Turaev-Viro的特征状态下的turaev-viro公式，对$ d+1 $ dimensions中的拓扑场理论的表述（TQFT $ _ {d+_ {d+1} $）和一个TQFT。通常，与symmetric-tqft $ _d $相对应的精确特征状态从tqft $ _ {d+1} $中的Frobenius代数跟随。对于$ d = 2 $，我们构建了准确产生2D有理CFT路径综合的本征状态，这奇怪地将连续的场理论路径综合与Turaev-Viro态态相关联。我们还设计并说明了$ d = 2,3 $的数值方法，以搜索cft $ _d $作为对称tqft $ _d $之间的相变点。最后，由于RG运算符实际上是一个精确的分析全息张量网络，因此我们计算``Bulk-Boundary''相关器，并与ADS/CFT字典进行比较，$ d = 2 $。鉴于我们的准确性，尽管需要进一步的工作来探索与ADS/CFT对应的确切连接，但它们在数值上是兼容的。
We show that the path-integral of conformal field theories in $D$ dimensions (CFT$_D$) can be constructed by solving for eigenstates of an RG operator following from the Turaev-Viro formulation of a topological field theory in $D+1$ dimensions (TQFT$_{D+1}$), explicitly realising the holographic sandwich relation between a symmetric theory and a TQFT. Generically, exact eigenstates corresponding to symmetric-TQFT$_D$ follow from Frobenius algebra in the TQFT$_{D+1}$. For $D=2$, we constructed eigenstates that produce 2D rational CFT path-integral exactly, which, curiously connects a continuous field theoretic path-integral with the Turaev-Viro state sum. We also devise and illustrate numerical methods for $D=2,3$ to search for CFT$_D$ as phase transition points between symmetric TQFT$_D$. Finally since the RG operator is in fact an exact analytic holographic tensor network, we compute ``bulk-boundary'' correlator and compare with the AdS/CFT dictionary at $D=2$. Promisingly, they are numerically compatible given our accuracy, although further works will be needed to explore the precise connection to the AdS/CFT correspondence.
