Exponentially Small Couplings between Twisted Fields of Orbifold String Theories

TL;DR

This paper explores how exponentially small couplings naturally arise between twisted fields in orbifold string theories, due to massive mode propagation and geometric separation, impacting effective field theories from higher dimensions.

Contribution

It provides a calculation of the tiny couplings between twisted fields in Z_3 orbifold compactifications of heterotic string theory, highlighting their exponential dependence on geometric and mass parameters.

Findings

Couplings are exponentially suppressed by the mass of intermediate states.

Small couplings depend on the distance between fixed points.

Propagation of Kaluza-Klein modes explains the weak interactions.

Abstract

We investigate the natural occurence of exponentially small couplings in effective field theories deduced from higher dimensional models. We calculate the coupling between twisted fields of the Z_3 Abelian orbifold compactification of the heterotic string. Due to the propagation of massive Kaluza-Klein modes between the fixed points of the orbifold, the massless twisted fields located at these singular points become weakly coupled. The resulting small couplings have an exponential dependence on the mass of the intermediate states and the distance between the fixed points.