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

The Frobenius-Schur indicator in Conformal Field Theory

An analogue of the classical Frobenius-Schur indicator is introduced in order to distinguish between real and pseudo-real self-conjugate primary fields, and an explicit expression for this quantity is derived from the trace of the braiding operator.Comment: 5 pages, TeX, some typos correcte

Frobenius-Schur Indicators, the Klein-bottle Amplitude, and the Principle of Orbifold Covariance

The "orbifold covariance principle", or OCP for short, is presented to support a conjecture of Pradisi, Sagnotti and Stanev on the expression of the Klein- bottle amplitude.Comment: 5 page

Galois currents and the projective kernel in Rational Conformal Field Theory

The notion of Galois currents in Rational Conformal Field Theory is introduced and illustrated on simple examples. This leads to a natural partition of all theories into two classes, depending on the existence of a non-trivial Galois current. As an application, the projective kernel of a RCFT, i.e. the set of all modular transformations represented by scalar multiples of the identity, is described in terms of a small set of easily computable invariants

Frobenius-Schur Indicators and Exponents of Spherical Categories

We obtain two formulae for the higher Frobenius-Schur indicators: one for a spherical fusion category in terms of the twist of its center and the other one for a modular tensor category in terms of its twist. The first one is a categorical generalization of an analogous result by Kashina, Sommerhauser, and Zhu for Hopf algebras, and the second one extends Bantay's 2nd indicator formula for a conformal field theory to higher degree. These formulae imply the sequence of higher indicators of an object in these categories is periodic. We define the notion of Frobenius-Schur (FS-)exponent of a pivotal category to be the global period of all these sequences of higher indicators, and we prove that the FS-exponent of a spherical fusion category is equal to the order of the twist of its center. Consequently, the FS-exponent of a spherical fusion category is a multiple of its exponent, in the sense of Etingof, by a factor not greater than 2. As applications of these results, we prove that the exponent and the dimension of a semisimple quasi-Hopf algebra H have the same prime divisors, which answers two questions of Etingof and Gelaki affirmatively for quasi-Hopf algebras. Moreover, we prove that the FS-exponent of H divides dim(H)^4. In addition, if H is a group-theoretic quasi-Hopf algebra, the FS-exponent of H divides dim(H)^2, and this upper bound is shown to be tight.Comment: 32p. LaTex file with macros and figures. Some typos and Thm 8.4 in v2 have been corrected. The current Thm 8.4 is a combined result of Thms 8.4 and 8.5 in version

FC Sets and Twisters: The Basics of Orbifold Deconstruction

We present a detailed account of the properties of twisters and their generalizations, FC sets, which are essential ingredients of the orbifold deconstruction procedure aimed at recognizing whether a given conformal model may be obtained as an orbifold of another one, and if so, to identify the twist group and the original model. The close analogy with the character theory of finite groups is discussed, and its origin explained.Comment: 26 page