W.A. Sabra

MODULAR SYMMETRIES, THRESHOLD CORRECTIONS AND MODULI FOR ℤ2 × ℤ2 ORBIFOLDS

ℤ2 × ℤ2 Coxeter orbifolds are constructed with the property that some twisted sectors have fixed planes for which the six-torus cannot be decomposed into a direct sum T2 ⊕ T4 with the fixed plane lying in T2. The string loop threshold corrections to the gauge coupling constants are derived, and display symmetry groups for the T and U moduli that are subgroups of the full modular group PSL(2, ℤ). The effective potential for duality invariant gaugino condensate in the presence of hidden sector matter is constructed and minimized for the values of the moduli. The effect of Wilson lines on the modular symmetries is also studied.

String Loop Threshold Corrections For ZN Coxeter Orbifolds.

The moduli dependence of string loop threshold corrections to gauge coupling constants is investigated for those ZN Coxeter orbifolds with the property that some twisted sectors have fixed planes for which the six-torus T6 cannot be decomposed into a direct sum T4 ⊕ T2 with the fixed plane lying in T2.

Duality Symmetries in Orbifold Models.

Abstract We derive the duality symmetries relevant to moduli dependent gauge coupling constant threshold corrections, in Coreter Z N orbifolds. We consider those orbifolds for which the point group leaves fixed a two-dimensional sublattice Λ 2 , of the six-dimensional torus lattice Λ 6 , where Λ 6 cannot be decomposed as Λ 2 ⊗ Λ 4 .

Spontaneous breaking of CP symmetry by orbifold moduli.

Abstract CP-violating phases which contribute to the electric dipole moment (EDM) of the neutron are considered in the context of orbifold compactification of the heterotic string. In particular, we study the situation where CP is spontaneously broken by moduli fields acquiring, in general, complex expectation values at the minimum of duality invariant low energy effective potentials. We show, by explicit minimization of such a potential in the case of the Z 6 - IIb orbifold, that it is the presence of so called Green-Schwarz anomaly coefficients δ GS i , that leads to significant CP violating expectation values of the moduli. By evaluating the soft supersymmetry breaking moduli dependent A and B terms in this model, we find that the experimental bounds Φ ( A ), Φ ( B ) −3 are exceeded for a particular range of values of the auxiliary field of the S modulus.

Symplectic embeddings and special Kähler geometry of CP(n − 1, 1)

The embedding of the isometry group of the coset spaces SU(1,n)/ U(1)xSU(n) in Sp(2n+2,R) is discussed. The knowledge of such embedding provides a tool for the determination of the holomorphic prepotential characterizing the special geometry of these manifolds and necessary in the superconformal tensor calculus of N=2 supergravity. It is demonstrated that there exists certain embeddings for which the homogeneous prepotential does not exist. Whether a holomorphic function exists or not, the dependence of the gauge kinetic terms on the scalars characterizing these coset in N=2 supergravity theory can be determined from the knowledge of the corresponding embedding, `a la Gaillard and Zumino. Our results are used to study some of the duality symmetries of heterotic compactifications of orbifolds with Wilson lines.

Modular Symmetries in ZN Orbifold Compactified String Theories with Wilson Lines .

Target space modular symmetries relevant to string loop threshold corrections are studied for ZN orbifold compactified string theories containing Wilson line background fields.

Anisotropic Solutions For Orbifold Moduli From Duality Invariant Gaugino Condensates.

The values of the T and U moduli are studied for those ZN Coxeter orbifolds with the property that some of the twisted sectors have fixed planes for which the six-torus T6 cannot be decomposed into a direct sum T2⊕T4 with the fixed plane lying in T2. Such moduli in general transform under a subgroup of the modular group SL(2,ℤ). The moduli are determined by minimizing the effective potential derived from a duality invariant gaugino condensate.

Twisted sector Yukawa couplings for the ZM × ZN orbifolds

Abstract The moduli dependent Yukawa couplings between twisted sectors of Z M × Z N Coxeter orbifolds are studied.

Yukawa couplings involving excited twisted-sector states for ZN and ZM × ZN orbifolds

We study the Yukawa couplings among excited twist fields which might arise the low-energy effective field theory obtained by compactifying the heterotic string on ZN and ZM × ZN orbifolds.

Kähler potentials for orbifolds with continuous Wilson lines and the symmetries of the string action

Abstract By employing the symmetries of the underlying conformal field theory, the tree-level Kahler potentials for untwisted moduli of the heterotic string compactifications on orbifolds with continuous Wilson lines are derived. These symmetries act linearly on bosonic (toroidal and E 8 × E 8 gauge) string coordinates as well as on the untwisted (toroidal and continuous Wilson lines) moduli; they correspond to the scaling of toroidal moduli, the axionic shift of toroidal moduli and the shift of the continuous Wilson line moduli. In turn such symmetries provide sufficient constraints to determine the form of the low-energy effective action associated with the untwisted moduli up to a multiplicative factor.