NUCLEAR Nuclear Physics B397 (1993) 379—4 14 P H VS I CS B North-Holland ________________ Higher twisted sector couplings of ~ N orbifolds * J. Erler a,b, D. Jungnickel a,b, M. Spaliñski b,1 and S. Stieberger b Max-Planck-Institut für Physik — Wemer-Heisenberg-Institut, P.O. Box 401212, W-8000 Munich, FRG “Physik Department, Technische Universitiit München, W-8046 Garching, FRG Received 29 July 1992 (Received 10 November 1992) Accepted for publication 20 November 1992 We derive the basic correlation functions of twist fields coming from arbitrary twisted sectors in symmetric 7~N orbifold conformal field theories, keeping all the admissible marginal perturba- tions, 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 mathe- matical point of view as they represent automorphic functions for a large class of discrete groups. 1. Introduction It was recognized some years ago that string theory could be a viable framework for gravity as well as other interactions. At that time it was already clear that compared to ordinary local field theory it is much more restrictive. This lead to the belief that this framework would be restrictive enough to select a more or less unique “Theory of Everything” [1]. It has since become clear that the existing (perturbative) formulation does, however, admit a great deal of arbitrariness concerning the vacuum state of string theory, which is of course reflected in the low-energy effective field theory. One of the tasks of the string phenomenologist is to determine which field theories can be interpreted as a low-energy description of a string compactification. The arbitrariness inherent in the presently available formulation of string theory is very poorly understood. In a generic compactification it manifests itself in the dependence of physical quantities on a set of parameters — the moduli [21. It is * Supported by the Deutsche Forschungsgemeinschaft. 1 Alexander von Humboldt Fellow. On leave from the Institute of Theoretical Physics, Warsaw University, PL-00 681 Warsaw, Poland. 0550-3213/93/$06.00 © 1993 — Elsevier Science Publishers B.V. All rights reserved