Kaluza-Klein masses in nonprime orbifolds: Z(12-I) compactification and threshold correction

TL;DR

This paper investigates Kaluza-Klein states and threshold corrections in non-prime orbifold compactifications of heterotic string theory, highlighting the role of Wilson lines and differences from field theory approaches.

Contribution

It provides a detailed analysis of KK states and threshold corrections in Z(12-I) orbifolds, incorporating Wilson line effects and clarifying distinctions from field theoretic models.

Findings

KK states arise only in non-prime orbifolds with large extra dimensions.

Threshold corrections include Wilson line effects and differ from field theory predictions.

GSO projection conditions are relaxed above the compactification scale.

Abstract

Analyzing the one-loop partition function, we discuss possible Kaluza-Klein (KK) states in the orbifold compactification of the heterotic string theory, toward the application to the threshold correction. The KK massive states associated with (relatively) large extra dimensions can arise only in non-prime orbifolds. The GSO projection condition by a shift vector $V^I$ is somewhat relaxed above the compactification scale 1/R. We also present the other condition on Wilson line $W$, $P\cdot W={\rm integer}$. With the knowledge of the partition function, we obtain the threshold corrections to gauge couplings, which include the Wilson line effects. We point out the differences in string and field theoretic orbifolds.