Explicit modular formulae and symmetries of RCFT's I

TL;DR

This paper derives explicit modular transformation formulae for Wess-Zumino characters in rational conformal field theories, focusing on algebra A_1 at positive level, and introduces new theorems on RCFT symmetries.

Contribution

It provides compact formulae for modular transformations and new theorems on RCFT symmetries, enhancing understanding of algebra A_1 at positive levels.

Findings

Derived explicit modular transformation formulae for WZ characters.

Identified isometry groups and genus formulas for algebra A_1 at positive level.

Formulated and proved new theorems on RCFT symmetries.

Abstract

We derive compact formulae for modular transformations of WZ characters. We start with algebra A_1 at positive level k=n-2, for which we can easily provide some description of isometry group and genus formula in a special case. We also point to general features, formulating and proving theorems for RCFT's which seem new.