Modular symmetries of threshold corrections for abelian orbifolds with discrete Wilson lines

Abstract

The modular symmetries of string loop threshold corrections for gauge coupling constants are studied in the presence of discrete Wilson lines for all examples of abelian orbifolds, where the point group is realised by the action of Coxeter elements or generalised Coxeter elements on the root lattices of the Lie groups.

Moduli stabilization and supersymmetry breaking in heterotic orbifold string models

“…In deriving the form of W np , however, we have neglected the fact that the presence of discrete Wilson lines often break the modular group SL(2, Z)to one of its subgroups. It has been noted [66] that turning on one or more Wilson lines breaks the modular group SL(2, Z) down to one of its subgroups. Define the subgroup Γ 0 (p) ⊂ SL(2, Z).…”

On moduli stabilisation and de Sitter vacua in MSSM heterotic orbifolds

“…The Wilson lines in the second and third planes break the symmetry in those directions down to congruence subgroups, which can be computed by solving the constraints eqs. (48)(49)(50)(51)(52)(53)(54)(55) found in the first reference of [36,37]. In the second plane the result is Γ 1 (3).…”

“…Some of these are: (i) the terms in the action are almost completely determined with very few free parameters (which come mainly from the little studied physics that decouples exotics), (ii) the modular symmetry groups are generically broken from SL (2, ) to some congruence subgroup due to the presence of Wilson lines [34][35][36][37], (iii) it is typically difficult to find more than one condensing gauge group, especially without decoupling hidden matter (since the latter tends to destroy asymptotic freedom), and subsequently, it is hard (but not impossible) to find dilatonic racetrack models, (iv) the moduli-dependent threshold corrections to the gauge couplings often do not appear with the required sign to force compactification, (v) it is not justified to take a universal Kähler modulus, and moreover the dynamics of all the bulk moduli are highly coupled together. All these features make the search for a metastable (de Sitter) vacuum more challenging than previously thought and our results underline this.…”

“…The presence of discrete Wilson line backgrounds breaks the modular symmetries down to the subgroup that leaves the Wilson line invariant [34][35][36][37]. Typically, the surviving modular symmetries are congruence subgroups of SL(2, Z), which further restrict the integer parameters, a, b, c, d, of the transformations.…”

“…Typically, the surviving modular symmetries are congruence subgroups of SL(2, Z), which further restrict the integer parameters, a, b, c, d, of the transformations. They can be computed by solving the constraints found in [36,37]. For instance, the groups that we encounter below are…”