Orbifold Conformal Field Theories Research Articles

Intertwiners in orbifold conformal field theories

Following on from earlier work relating modules of meromorphic bosonic conformal field theories to states representing solutions of certain simple equations inside the theories, we show, in the context of orbifold theories, that the intertwiners between twisted sectors are unique and described explicitly in terms of the states corresponding to the relevant modules. No explicit knowledge of the structure of the twisted sectors is required. Further, we propose a general set of sufficiency conditions, illustrated in the context of a third-order no-fixed-point twist of a lattice theory, for verifying consistency of arbitrary orbifold models in terms of the states representing the twisted sectors.

Higher twisted sector couplings of [formula omitted] orbifolds

We derive the basic correlation functions of twist fields coming from arbitrary twisted sectors in symmetric Z N orbifold conformal field theories, keeping all the admissible marginal perturbations, in particular those corresponding to the antisymmetric-tensor background field. This allows a thorough investigation of modular symmetries in this type of string compactification. Such a study is explicitly carried out for the group generated by duality transformations. Thus, apart from being of phenomenological use, our couplings are also interesting from the mathematical point of view as they represent automorphic functions for a large class of discrete groups.

The nonperturbative analysis of background duality in orbifold conformal field theory

We study duality in simple two-dimensional orbifold models with metric and axionic backgrounds at arbitrary orders in string perturbation theory. It is shown that duality involves certain linear relations among twist correlators at dual backgrounds which are independent of the perturbative order. Relying on methods of harmonic analysis, a nonperturbative representation (in the sense of string field theory) of a class of S-matrix elements is obtained in terms of a universal background-independent spectral distribution and nonholomorphic modular vector functions of the background parameters. At the same time, we find new realizations of the Verlinde algebra and of hypergroups characterizing the S-matrix nonperturbatively. Various examples and calculations are worked out.

An operator formulation of orbifold conformal field theory

In many applications of conformal field theory one encounters twisted conformal fields, i.e. fields which have branch cut singularities on the relevant Riemann surfaces. We present a geometrical framework describing twisted conformal fields on Riemann surfaces of arbitrary genus which is alternative to the standard method of coverings. We further illustrate the theory of twisted Grassmannians and its relation with the representation theory of the twisted oscillator algebras. As an application of the above, we expound an operator formalism for orbifold strings.

Covariance properties of higher genus twist correlators under [formula omitted] durability in orbifold conformal field theory

We study R↔ 1 R duality in simple orbifold models at arbitrary orders in string perturbation theory. It is shown that duality involves certain linear relations among twist correlators at dual radii. We derive general expressions for the coefficients of these relations and show that they can be expressed in terms of functions of the orbifold cosets obeying an algebra bearing a striking resemblance to Verlinde's fusion rule algebra. Finally, we study the behavior of the coefficients under factorization, in particular their dependence on the genus. A few examples are worked out.

The conformal field theory of orbifolds

A prescription for the calculation of any correlation function in orbifold conformal field theory is given. The method is applied to the scattering of four twisted string states, which allows the extraction of operator product coefficients of conformal twist fields. We derive Yukawa couplings in the effective field theory for fermionic strings on orbifolds.