On examples of intermediate subfactors from conformal field theory

TL;DR

This paper classifies intermediate subfactors in conformal field theory settings, confirming a generalized Wall's conjecture across multiple series of conformal inclusions and related structures.

Contribution

It provides a comprehensive classification of intermediate subfactors for specific conformal inclusions and verifies a generalized Wall's conjecture within this framework.

Findings

All intermediate subfactors for four series of conformal inclusions are determined.

The generalized Wall's conjecture is verified for these subfactors.

Results extend to Jones-Wassermann subfactors from Loop group representations.

Abstract

Motivated by our subfactor generalization of Wall's conjecture, in this paper we determine all intermediate subfactors for conformal subnets corresponding to four infinite series of conformal inclusions, and as a consequence we verify that these series of subfactors verify our conjecture. Our results can be stated in the framework of Vertex Operator Algebras. We also verify our conjecture for Jones-Wassermann subfactors from representations of Loop groups extending our earlier results.