Fusion symmetric spaces and subfactors

TL;DR

This paper constructs fusion category analogs of classical group embeddings, explores their applications in boundary conformal field theory, and calculates key invariants of associated subfactors.

Contribution

It introduces new fusion category constructions mimicking classical group embeddings and analyzes their unitarizability and subfactor invariants.

Findings

Identified conditions for unitarizability of the categories

Explicitly calculated the index of the subfactors

Determined the principal graphs associated with these subfactors

Abstract

We construct analogs of the embedding of orthogonal and symplectic groups into unitary groups in the context of fusion categories. At least some of the resulting module categories also appear in boundary conformal field theory. We determine when these categories are unitarizable, and explicitly calculate the index and principal graph of the resulting subfactors.