Comments on the Links between su(3) Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards

Abstract

We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain algebraic curves related to triangular billiards, their meaning remains obscure. In an attempt to go beyond the su(3) case, we show that any rational conformal field theory determines canonically a Riemann surface.

56 pages, 4 eps figures, LaTeX, uses epsf

References in corpus (5)

• Galois Modular Invariants of WZW Models
• WZW Commutants, Lattices, and Level 1 Partition Functions
• Automorphism Modular Invariants of Current Algebras
• Implications of an arithmetical symmetry of the commutant for modular invariants
• Towards a Classification of su(2)$⨁\cdots ⨁$su(2) Modular Invariant Partition Functions

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• Discrete symmetries of unitary minimal conformal theories
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• The W_N minimal model classification
• On parity functions in conformal field theories
• Galois currents and the projective kernel in Rational Conformal Field Theory
• Higher Rank TQFT Representations of SL(2,Z) are Reducible
• Character Vectors of Strongly Regular Vertex Operator Algebras