The Untwisted Stabilizer in Simple Current Extensions

A method is presented to compute the order of the untwisted stabilizer of a simple current orbit, as well as some results about the properties of the resolved fields in a simple current extension.Comment: 6 pages, LaTe

Algebraic Aspects of Orbifold Models

: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the quantum group is presented.Comment: 22, ITP-Budapest 49

Simple Current Extensions and Mapping Class Group Representations

The conjecture of Fuchs, Schellekens and Schweigert on the relation of mapping class group representations and fixed point resolution in simple current extensions is investigated, and a cohomological interpretation of the untwisted stabilizer is given.Comment: 12 pages, LaTeX, references update

Characters and modular properties of permutation orbifolds

Explicit formulae describing the genus one characters and modular transformation properties of permutation orbifolds of arbitrary Rational Conformal Field Theories are presented, and their relation to the theory of covering surfaces is investigated.Comment: 7 pages, LaTe

Character relations and replication identities in 2d Conformal Field Theory

We study replication identities satisfied by conformal characters of a 2D CFT, providing a natural framework for a physics interpretation of the famous Hauptmodul property of Monstrous Moonshine, and illustrate the underlying ideas in simple cases.Comment: Some references added and conclusions greatly expande

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

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