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

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

1996-04-18

arxiv.org/abs/hep-th/9604104v1

J.Geom.Phys. 22 (1997) 134-189

Physics

High Energy Physics

High Energy Physics - Theory

56 pages, 4 eps figures, LaTeX, uses epsf

Scientific paper

10.1016/S0393-0440(96)00027-7

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.

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