Higher Twisted Sector Couplings of $Z_N$ Orbifolds

TL;DR

This paper derives correlation functions of twist fields in symmetric Z_N orbifold conformal field theories, exploring modular symmetries and automorphic properties relevant for string compactifications.

Contribution

It provides explicit calculations of twist sector couplings including marginal perturbations, enhancing understanding of modular symmetries in orbifold models.

Findings

Derived correlation functions for arbitrary twisted sectors.

Analyzed modular symmetries and duality transformations.

Couplings as automorphic functions for discrete groups.

Abstract

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.