Bert Schellekens

Instanton induced neutrino Majorana masses in CFT orientifolds with MSSM-like spectra

Recently it has been shown that string instanton effects may give rise to neutrino Majorana masses in certain classes of semi-realistic string compactifications. In this paper we make a systematic search for supersymmetric MSSM-like Type II Gepner orientifold constructions admitting boundary states associated with instantons giving rise to neutrino Majorana masses and other L- and/or B-violating operators. We analyze the zero mode structure of D-brane instantons on general type II orientifold compactifications, and show that only instantons with O(1) symmetry can have just the two zero modes required to contribute to the 4d superpotential. We however discuss how the addition of fluxes and/or possible non-perturbative extensions of the orientifold compactifications would allow

Orientifolds, hypercharge embeddings and the Standard Model

Abstract The embedding of the SM hypercharge into an orientifold gauge group is studied. Possible embeddings are classified, and a systematic construction of bottom–up configurations and top–down orientifold vacua is achieved, solving the tadpole conditions in the context of Gepner orientifolds. Some hypercharge embeddings are strongly preferred compared to others. Configurations with chiral anti-symmetric tensors are suppressed. We find among others, genuine examples of supersymmetric SU ( 5 ) , flipped SU ( 5 ) , Pati–Salam and trinification vacua with no chiral exotics.

From Dynkin diagram symmetries to fixed point structures

Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra g induces an automorphism of g and a mappingτω between highest weight modules of g. For a large class of such Dynkin diagram automorphisms, we can describe various aspects of these maps in terms of another Kac-Moody algebra, the “orbit Lie algebra” ğ. In particular, the generating function for the trace ofτω over weight spaces, which we call the “twining character” of g (with respect to the automorphism), is equal to a character of ğ. The orbit Lie algebras of untwisted affine Lie algebras turn out to be closely related to the fixed point theories that have been introduced in conformal field theory. Orbit Lie algebras and twining characters constitute a crucial step towards solving the fixed point resolution problem in conformal field theory.

THE RESOLUTION OF FIELD IDENTIFICATION FIXED POINTS IN DIAGONAL COSET THEORIES

The fixed point resolution problem is solved for diagonal coset theories. The primary fields into which the fixed points are resolved are described by submodules of the branching spaces, obtained as eigenspaces of the automorphisms that implement field identification. To compute the characters and the modular S-matrix we use ‘orbit Lie algebras’ and ‘twining characters’, which were introduced in a previous paper [1]. The characters of the primary fields are expressed in terms branching functions of twining characters. This allows us to express the modular S-matrix through the S-matrices of the orbit Lie algebras associated to the identification group. Our results can be extended to the larger class of ‘generalized diagonal cosets’.

SU(5) orientifolds, Yukawa couplings, Stringy Instantons and Proton Decay

Abstract We construct a large class of SU ( 5 ) orientifold vacua with tadpole cancellation both for the standard and the flipped case. We give a general analysis of superpotential couplings up to quartic order in orientifold vacua and identify the properties of needed Yukawa couplings as well as the baryon number violating couplings. We point out that successful generation of the perturbatively forbidden Yukawa couplings entails a generically disastrous rate for proton decay from an associated quartic term in the superpotential, generated from the same instanton effects. We search for the appropriate instanton effects that generate the missing Yukawa couplings in the SU ( 5 ) vacua we constructed and find them in a small subset of them.

Discriminating MSSM families in (free-field) Gepner Orientifolds

A complete analysis of orientifold compactifications involving Gepner models that are free fields (k=1,2) is performed. A set of tadpole solutions is found that are variants of a single chiral spectrum. The vacua found have the property that different families have different U(1) charges so that one family cannot obtain masses in perturbation theory. Its masses must come from instantons, allowing for a hierarchy of masses. The phenomenological aspects of such vacua are analyzed.

Free Fermion Orientifolds

We investigate a class of orientifold models based on tensor products of 18 Ising models. Using the same search criteria as for the comparable case of Gepner model orientifolds we find that there are no three-family standard model configura- tions with tadpole cancellation. Even if we do not impose the latter requirement, we only find one such configuration in the special case of complex free fermions. In order to allow a comparison with other approaches we enumerate the Hodge numbers of the type-IIB theories we obtain. We provide indications that there are fermionic IIB vacua that are not Z2 ×Z2 orbifolds.

Modular invariants and fusion rule automorphisms from Galois theory

Abstract We show that Galois theory of cyclotomic number fields provides a powerful tool to construct systematically integer-valued matrices commuting with the modular matrix S , as well as automorphisms of the fusion rules. Both of these prescriptions allow the construction of modular invariants and offer new insight in the structure of known exceptional invariants.

Trace formulas for Annuli

Assuming the completeness condition for boundaries we derive trace formulas for the annulus coefficients in 2-dimensional conformal field theory. We also derive polynomial equations that relate the annulus, Moebius and Klein bottle coefficients, and conjecture an annulus trace formula that is sensitive to the orientation of the boundaries.

Quasi-Galois Symmetries of the Modular S-Matrix

The recently introduced Galois symmetries of rational conformal field theory are generalized, for the case of WZW theories, to “quasi-Galois symmetries.” These symmetries can be used to derive a large number of equalities and sum rules for entries of the modular matrixS, including some that previously had been observed empirically. In addition, quasi-Galois symmetries allow us to construct modular invariants and to relateS-matrices as well as modular invariants at different levels. They also lead us to a convenient closed expression for the branching rules of the conformal embeddings.