String emission from twisted sectors: Cocycle operators and modular background symmetries

In this work, the authors compute coupling constants for the emission of untwisted states within the class of even dimensional, bosonic orbifolds. In order to apply the operator formalism they first have to construct the untwisted and twisted sector cocycle operators which complete the zero mode part of vertex operators. Their existence is guaranteed by a consistency condition on the axionic background whose general solution will be determined. These results enable study of various discrete background maps (duality, shifts of axionic components) which reshuffle the vertices. The authors then recognize that the process of the emission of strings from whichever twisted sector provides a modular invariant