Threshold corrections in orbifold models and superstring unification of gauge interactions

Abstract

The string one loop renormalization of the gauge coupling constants is examined in abelian orbifold models. The contributions to string threshold corrections independent of the compactification moduli fields are evaluated numerically for several representative examples of orbifold models. We consider cases with standard and non-standard embeddings as well as cases with discrete Wilson lines background fields which match reasonably well with low energy phenomenology. The gap separating the observed grand unified theories scale M GUT ≃ 2 × 10 16 GeV from the string unification scale M X ≃ 5 × 10 17 GeV is discussed on the basis of standard-like orbifold models. We examine one loop gauge coupling constants unification in a description incorporating the combined effects of moduli dependent and independent threshold corrections, an adjustable affine level for the hypercharge group factor and a large mass threshold associated with an anomalous U (1) mechanism.

String theory and the path to unification: A review of recent developments

“…For example, the mechanisms that give rise to large threshold corrections may not be realizable or mutually consistent with the mechanisms that give rise to other desirable phenomenological features such as the appearance of N = 1 spacetime supersymmetry or three generations. Many previous calculations of the threshold corrections have been performed for various types of orbifold or free-fermionic models [19,82,62,83,74], but in most cases such models were typically not phenomenologically realistic. Indeed, the increased complexity of the realistic string models may substantially alter previous expectations.…”

Systematics of string loop threshold corrections in orbifold models

“…Thus, a simple-minded explanation for the standard model gauge coupling constant unification, as being solely due to heavy threshold corrections is ruled out. The new revised results leave the initial conclusions [20,21] unchanged. The scenarios for perturbative string theory unification appealing to the combined effects of affine algebra levels, anomalous U(1) factor and enhanced threshold corrections from large compactification volumes should continue to provide a viable alternative.…”

“…Several studies of threshold corrections using solvable models of string vacua have attempted to justify a decomposition of this type [21]. In this section, we shall pursue the effort started in our previous paper [20] with the purpose of updating the numerical results reported there for the gauge coupling constants by use of the more complete formalism presented in the previous section. We perform numerical calculations for the following selection of 16 abelian orbifold models: (i) The seven standard embedding Z N orbifolds described for N = 3, 4, 6, by the internal shift vectors, Nv i = (1, 1, −2); for N = 7, 8, by Nv i = (1, 2, −3); and for N = 12 by Nv i = (1, 4, −5); (ii) Four non-standard embedding models described by the gauge sector shifts, (NV I )(NV ′ I ) = (1120 5 )(1120 5 ) ′ , (110 6 )(20 7 ) ′ , (1 4 20 3 )(20 7 ) ′ , for Z 3 , and (1120 5 )(220 6 ) ′ for Z 4 ; (iii) Three non-standard embedding Z 3 models with two discrete Wilson lines, due to Ibáñez et al, [69] and Kim and Kim [70].…”

“…(27), in powers of the the gauge and gravitational field strength parameters, F a , R, using eq. (20) to describe the perturbed conformal weights. The power expansion up to quartic order is: We have omitted, for simplicity, the mixed power terms, O(F n R m ), and used the following abbreviations:Q ′ =Q +Ī 3 , K = k + 2, t = 8πτ 2 .…”

“…The approach initiated in [2,3], and developed further in [4,5,6,7,8,9,10,11,12], has served an important purpose in testing the string theory dualities [13,14]. It has also been applied in several phenomenological studies [15,16,17,18,19,20,21]. Recently, a more complete approach was presented by Kiritsis and Kounnas [22].…”