Peter Bantay

Characters and modular properties of permutation orbifolds

Abstract 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.

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.

Symmetric Products, Permutation Orbifolds and Discrete Torsion

Symmetric product orbifolds, i.e. permutation orbifolds of the full symmetric group Sn are considered by applying the general techniques of permutation orbifolds. Generating functions for various quantities, e.g. the torus partition functions and the Klein-bottle amplitudes are presented, as well as a simple expression for the discrete torsion coefficients.

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.

Self-organization and anomalous diffusion

The self-organizing process is investigated in the continuum limit of the cellular automaton model introduced by Bak, Tang and Wiesenfeld. An anomalous diffusion equation is proposed for the description of this process, and an analytical method for the solutionis presented in one dimension, based on an adiabatic approximation.

Orbifolds, Hopf algebras, and the Moonshine

We describe the modular properties and fusion rules of holomorphic orbifold models by Hopf algebraic techniques, using the representation theory of the orbifold quantum group. We apply this theory to the construction of generalized Thompson series, and discuss its connections with Moonshine.

Conformal characters and the modular representation

A general procedure is presented to determine, given any suitable representation of the modular group, the characters of all possible Rational Conformal Field Theories whose associated modular representation is the given one. The relevant ideas and methods are illustrated on two non-trivial examples: the Yang-Lee and the Ising models.

MAPPING CLASS GROUP REPRESENTATIONS AND GENERALIZED VERLINDE FORMULA

Unitary representations of centrally extended mapping class groups , g ≥ 1 are given in terms of a rational Hopf algebra H, and a related generalization of the Verlinde formula is presented. Formulae expressing the traces of mapping class group elements in terms of the fusion rules, quantum dimensions and statics phases are proposed.

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.

Orbifoldization, Covering Surfaces and Uniformization Theory

The connection between the theory of permutation orbifolds, covering surfaces, and uniformization is investigated, and the higher genus partition functions of an arbitrary permutation orbifold are expressed in terms of those of the original theory.