Work

CFT D from TQFT D + 1 via Holographic Tensor Network, and Precision Discretization of CFT 2

Year: 2024

Type: article

Abstract: We show that the path integral of conformal field theories in D dimensions ( CFT D ) can be constructed by solving for eigenstates of a renormalization group (RG) operator following from the Turaev-Viro formulation of a topological field theory (topological quantum field theory) (TQFT) in D + 1 dimensions ( TQFT D + 1 ), explicitly realizing the holographic sandwich relation between a symmetric theory and a TQFT. Generically, exact eigenstates corresponding to symmetric TQFT D follow from Frobenius algebra in TQFT D + 1 . For D = 2 , we construct eigenstates that produce 2D rational CFT path integrals exactly, which curiously connect 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” correlators and compare them 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. Published by the American Physical Society 2024

Source: Physical Review X

DOI: 10.1103/physrevx.14.041033