Abstract
Extended chiral field theories with an internal quantum symmetry are characterized by a modular form M(τ) covariant under a subgroup Γ N 0ofΓ =SL(2,Z). This subgroup is known to be the modular group of a theory with twisted boundary To each modular invariant partition function Z of the ADE classification of corresponds a form M but some of the M's are images of two different Z's.
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