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The kernel of the modular representation and the Galois action in RCFT

P. Bantay
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Abstract

It is shown that for the modular representations associated to Rational Conformal Field Theories, the kernel is a congruence subgroup whose level equals the order of the Dehn-twist. An explicit algebraic characterization of the kernel is given. It is also shown that the conductor, i.e. the order of the Dehn-twist is bounded by a function of the number of primary fields, allowing for a systematic enumeration of the modular representations coming from RCFTs. Restrictions on the spectrum of the Dehn-twist and arithmetic properties of modular matrix elements are presented.

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P. Bantay. 2001-04-19. The kernel of the modular representation and the Galois action in RCFT. https://doi.org/10.1007/s00220-002-0760-x

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