Modular Invariance and Uniqueness of Conformal Characters

TL;DR

This paper demonstrates that conformal characters of rational W-algebra models are uniquely determined by central charge and conformal dimensions, and introduces tools for analyzing SL(2,Z) representations on modular functions.

Contribution

It provides a proof of uniqueness for conformal characters based on minimal data and develops new methods for studying SL(2,Z) actions on modular functions.

Findings

Conformal characters are uniquely determined by central charge and conformal dimensions.

Developed tools for analyzing SL(2,Z) representations on modular functions.

Methods may be applicable to a wide range of rational conformal field theories.

Abstract

We show that the conformal characters of various rational models of W-algebras can be already uniquely determined if one merely knows the central charge and the conformal dimensions. As a side result we develop several tools for studying representations of SL(2,Z) on spaces of modular functions. These methods, applied here only to certain rational conformal field theories, may be useful for the analysis of many others.