Realizations of pseudo bosonic theories with non-diagonal automorphisms

TL;DR

This paper proves that pseudo conformal field theories with non-diagonal automorphisms can be realized by rational conformal field theories, specifically free bosons, completing previous classifications and extending to characteristic 2 powers.

Contribution

It completes the classification of pseudo conformal field theories with non-diagonal automorphisms by showing their realization as free boson RCFTs in characteristic 2 cases.

Findings

For characteristics p ≠ 2, non-diagonal automorphisms are equivalent to diagonal cases.

For p=2^n, non-diagonal automorphisms are realizable as free boson RCFTs.

The classification of pseudo conformal field theories is extended to include these cases.

Abstract

Pseudo conformal field theories are theories with the same fusion rules, but with different modular matrix as some conventional field theory. One of the authors defined these and conjectured that, for bosonic systems, they can all be realized by some actual RCFT, which is of free bosons. We complete the proof here by treating the non diagonal automorphism case. It is shown that for characteristics $p\neq2$ they are all equivalent to a diagonal case, fully classified in our previous publication. For $p=2^n$ we realize the non diagonal case, establishing this theorem.