Quasi-Galois Symmetries of the Modular S-Matrix

TL;DR

This paper extends Galois symmetries to quasi-Galois symmetries in RCFT, enabling derivation of new sum rules, construction of modular invariants, and insights into conformal embeddings.

Contribution

It introduces quasi-Galois symmetries for WZW models, generalizing existing Galois symmetries, and applies them to derive sum rules, construct invariants, and conjecture branching rules.

Findings

Derived new sum rules for S-matrix entries.

Constructed modular invariants using quasi-Galois symmetries.

Proposed a conjecture for conformal embedding branching rules.

Abstract

The recently introduced Galois symmetries of RCFT are generalized, for the WZW case, to `quasi-Galois symmetries'. These symmetries can be used to derive a large number of equalities and sum rules for entries of the modular matrix S, including some that previously had been observed empirically. In addition, quasi-Galois symmetries allow to construct modular invariants and to relate S-matrices as well as modular invariants at different levels. They also lead us to an extremely plausible conjecture for the branching rules of the conformal embeddings of g into so(dim g).