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

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.