Constraints on asymmetric orbifolds

It is claimed that besides the left-right matching condition, one has to check the relative phases dictated by modular invariance for an asymmetric orbifold to give rise to an acceptable model.     

Gauge symmetries in heterotic asymmetric orbifolds

We study heterotic asymmetric orbifold models. By utilizing the lattice engineering technique, we classify (22,6)$(22,6)$-dimensional Narain lattices with right-moving non-Abelian group factors which can be starting points for _Z3${\mathbf{Z}}_3$ asymmetric orbifold construction. We also calculate gauge symmetry breaking patterns.     

K-Theory, Reality, and Orientifolds

We use equivariant K-theory to classify charges of new (possibly non-supersymmetric) states localized on various orientifolds in Type II string theory. We also comment on the stringy construction of new D-branes and demonstrate the discrete electric-magnetic duality in Type I brane systems with p+q=7, as proposed by Witten.     

Model building on asymmetric Z3 orbifolds: Non-supersymmetric models

Four-dimensional string models arising in the asymmetric Z₃ orbifold compactifications of the heterotic string are studied. A mechanism for supersymmetry breaking that gives rise to chiral models in four dimensions is presented, and some typical models are discussed. A formalism for calculating one-loop partition functions in Z₃ models is developed. One partition function is constructed that may correspond to a non-supersymmetric, tachyon-free theory, with a vanishing cosmological constant as a consequence of Atkin-Lehner symmetry. The negative result of a search for the model corresponding to this partition function is reported.     

Permutation orbifolds

A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for fusion rule coefficients are presented, together with the relevant mathematical concepts, such as Λ-matrices and twisted dimensions. The arithmetic restrictions implied by the theory for the allowed modular representations in CFT are discussed. The simplest nonabelian example with twist group S₃ is described to illustrate the general theory.     

Degenerate orbifolds

We present evidence for the existence of new four-dimensional string theories, obtained from a smooth variation of background fields in the twisted sectors of symmetric and asymmetric orbifolds. Flat directions only in the untwisted sector are shown to reproduce previously constructed models in terms of Wilson lines, exhibiting a Three-Higgs-Rule (THR). The new models provide a mechanism to lower the rank of the gauge group, lead to more flexible Yukawa couplings and give a strict separation of hidden and observable sectors, which are usually mixed in (2, 0)-models. Even though Fayet-Iliopoulos terms are induced in some of the models due to the presence of anomalous U(1)'s supersymmetry remains, in general, unbroken. Particular examples of the new models correspond to “blown up” versions of (2, 0)-orbifolds.     

On non-supersymmetric CFT in four dimensions

We show that the theories on the self-dual D3-branes of Type 0 string theory are in the class of the previously considered tadpole-free orbifolds of theory (although they have SO(6) global symmetry) and hence have vanishing beta function in the planar limit to all orders in 't Hooft coupling. Also, all planar amplitudes in this theory are equal to those of theory, up to a rescaling of the coupling.     

WZW Orientifolds and Finite Group Cohomology

The simplest orientifolds of the WZW models are obtained by gauging a symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted inversion , where ζ is an element of the center of G. It reverses the sign of the Kalb-Ramond torsion field H given by a bi-invariant closed 3-form on G. The action on the worldsheet reverses its orientation. An unambiguous definition of Feynman amplitudes of the orientifold theory requires a choice of a gerbe with curvature H on the target group G, together with a so-called Jandl structure introduced in [31]. More generally, one may gauge orientifold symmetry groups that combine the -action described above with the target symmetry induced by a subgroup Z of the center of G. To define the orientifold theory in such a situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We reduce the study of the existence of such structures and of their inequivalent choices to a problem in group-Γ cohomology that we solve for all simple simply connected compact Lie groups G and all orientifold groups . Membre du C.N.R.S.     

T-Duality for Orientifolds and Twisted KR-Theory

D-brane charges in orientifold string theories are classified by the KR-theory of Atiyah. However, this is assuming that all O-planes have the same sign. When there are O-planes of different signs, physics demands a “KR-theory with a sign choice” which up until now has not been studied by mathematicians (with the unique exception of Moutuou, who did not have a specific application in mind). We give a definition of this theory and compute it for orientifold theories compactified on S ¹ and T ². We also explain how and why additional “twisting” is implemented. We show that our results satisfy all possible T-duality relationships for orientifold string theories on elliptic curves, which will be studied further in subsequent work.     

Sphalerons on orbifolds

In this work, we study the electroweak sphalerons in a 5D background, where the fifth dimension lies on an interval. We consider two specific cases: flat space-time and the anti-de Sitter space-time compactified on S ¹/Z ₂. In our work, we take the SU(2) gauge–Higgs model, where the gauge fields reside in the 5D bulk; but the Higgs doublet is confined in one brane. We find that the results in this model are close to those of the 4D Standard Model (SM). The existence of the warp effect, as well as the heaviness of the gauge Kaluza–Klein modes make the results extremely close to the SM ones.     

Fat branes,orbifolds and doublet-triplet splitting

A simple higher dimensional mechanism of the doublet-triplet splitting is presented in a five dimensional supersymmetric SU(5) GUT on S¹/Z₂. The splitting of multiplets is realized by a mass term of the Higgs hypermultiplet which explicitly breaks SU(5) gauge symmetry. Depending on the sign of the mass, zero mode Higgs doublets and triplets are localized on either side of the fixed points. The mass splitting is realized due to the difference of magnitudes of the overlap with a brane localized or a bulk singlet field. No unnatural fine-tuning of the parameters is needed. The proton stability is ensured by locality - without symmetries.Received: 17 September 2003, Revised: 21 November 2003, Published online: 4 February 2004Nobuhito Maru: Special Postdoctoral Researcher     

Orientifolds of type IIA strings on Calabi-Yau manifolds

We identify type IIA orientifolds that are dual toM-theory compactifications on manifolds withG ₂-holonomy. We then discuss the construction of cross-cap states in Gepner models.     

Duality and orbifolds

We construct several examples where duality transformation commutes with the orbifolding procedure even when the orbifolding group does not act freely, and there are massless states from the twisted sector at a generic point in the moduli space. Often the matching of spectrum in the dual theories is a result of nontrivial identities satisfied by the coefficients on one loop tadpoles in the heterotic, type II and type I string theories.