Modular Invariance on the Torus and Fractional Quantum Hall Effect
نویسنده
چکیده
The implementation of modular invariance on the torus at the quantum level is discussed in a group-theoretical framework. Two cases must be considered, depending on the cohomology class of the symplectic form on the torus. If it is of integer cohomology class n, then full modular invariance is achieved at the quantum level only for those wave functions on the torus which are periodic if n is even, or antiperiodic if n is odd. If the symplectic form is of rational cohomology class nr , a similar result holds –the wave functions must be either periodic or antiperiodic on a torus r times larger in both direccions, depending on the parity of nr. Applications of these results to the abelian Chern-Simons theory and Fractional Quantum Hall Effect are discussed.
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