Modular Invariance and Uniqueness of Conformal Characters

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.

21 pages (AMS TeX), BONN-TH-94-16, MPI-94-67

References in corpus (6)

• W-symmetry in Conformal Field Theory
• Dilogarithm Identities in Conformal Field Theory
• How Complete is the Classification of W-Symmetries ?
• Path Spaces and W-Fusion in Minimal Models
• The vacuum preserving Lie algebra of a classical W-algebra
• Fusion Algebras Induced by Representations of the Modular Group

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• Hecke Relations in Rational Conformal Field Theory
• Holomorphic modular bootstrap revisited
• Product Expansions of Conformal Characters
• Modular flavor symmetry and vector-valued modular forms
• Modular differential equations for characters of RCFT
• Modular differential equations for torus one-point functions
• What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT
• Galois currents and the projective kernel in Rational Conformal Field Theory