Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders

Yoshiki Fukusumi, Guangyue Ji, Bo Yang

arXiv:2311.15621Physical review. B./Physical review. BMar 5, 20255 citations

Journal of Physics A Mathematical and General

Fermionic order and disorder variables and correlation functions

R. E. Gamboa Saraví, Eduardo C. Marino

Published Apr 7, 1991• 0 citations

Publisher

Abstract

Order and disorder operators and correlation functions are studied in the context of a fermionic quantum field theory in 1+1 dimensions.

DOI: 10.1088/0305-4470/24/7/029

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arXiv:2311.15621Physical review. B./Physical review. BMar 5, 20255 citations

In this paper, we revisit the operator-state correspondence in the Majorana conformal field theory (CFT) with emphasis on its semion representation. Whereas the semion representation (or

{Z}_{2}

extension of the chiral Ising CFT) gives a concise ``Abelian'' (or invertible) representation at the level of fusion rules and quantum states, there exists a subtlety when considering the chiral multipoint correlation function. In this sense, the operator-state correspondence in the semion sector of the fermionic theory inevitably contains a difficulty coming from its anomalous conformal dimension

1/16

as a

{Z}_{2}

symmetry operator. By analyzing the asymptotic behaviors of the existing correlation functions, we propose a nontrivial correspondence between the chiral conformal blocks and bulk correlation functions containing both order and disorder fields. One can generalize this understanding to

{Z}_{N}

models or fractional supersymmetric models (for which there exist long-standing open problems). We expect that this may improve our understanding of the simple current extension of CFT, which commonly appears in the studies of topologically ordered systems.