Oral: Simple current extension of chiral conformal field theories: General algebraic descriptions of topological orders or fractional quantum Hall systems

In these decades, it has been gradually established that the wavefunctions of topologically ordered systems correspond to the correlation functions of the corresponding chiral conformal field theories. This is known as bulk-edge correspondence in the condensed matter community or conformal field theory/topological quantum field theory (CFT/TQFT) correspondence in the high energy physics theory community.

Most of the chiral conformal field theories studied in the literature are bosonic chiral conformal field theories referred to as modular tensor categories (MTCs). However, MTCs are insufficient to study fractional quantum Hall systems because their underlying conformal field theories are not bosonic chiral conformal field theories. In this presentation, we demonstrate nontrivial aspects of the group extension of chiral conformal field theories based on fusion algebra. Our formulation is concise and applicable to general topologically ordered or quantum Hall systems.

As a concrete example, we study the Moore-Read states, the most famous non-abelian quantum Hall states, as Majorana fermionic chiral conformal field theory. We demonstrate the algebraic property of the system and demonstrate the breaking of operator-state correspondence even in this fundamental model. The latter is surprising but it is a natural consequence of simple current extension. Our findings open new research directions for chiral conformal field theories and the corresponding topological orders. This presentation is based on arXiv:2311.15621 and arXiv:2405.05178.