arXiv subjects
Publications and source records attributed to Gabriele Honecker.
We present the perturbative Yukawa couplings of the Standard Model on fractional intersecting D6-branes on T6/Z6' and discuss two mechanisms of creating mass terms for the vector-like particles in the matter spectrum, through perturbative three-point couplings and through continuous D6-brane displacements.
We systematically derive the perturbatively exact holomorphic gauge kinetic function, the open string Kaehler metrics and closed string Kaehler potential on intersecting D6-branes by matching open string one-loop computations of gauge thresholds with field theoretical gauge couplings in N=1 supergravity. We consider all cases of bulk, fractional and rigid D6-branes on T6/OR and the orbifolds T6/(Z(N)xOR) and T6/(Z(2)xZ(2M)xOR) without and with discrete torsion, which differ in the number of bulk complex structures and in the bulk Kaehler potential. Our analysis includes all supersymmetric configurations of vanishing and non-vanishing angles among D6-branes and O6-planes, and all possible Wilson line and displacement moduli are taken into account. The shape of the Kaehler moduli turns out to be orbifold independent but angle dependent, whereas the holomorphic gauge kinetic functions obtain three different kinds of one-loop corrections: a Kaehler moduli dependent one for some vanishing angle independently of the orbifold background, another one depending on complex structure moduli only for fractional and rigid D6-branes, and finally a constant term from intersections with O6-planes. These results are of essential importance for the construction of the related effective field theory of phenomenologically appealing D-brane models. As first examples, we compute the complete perturbative gauge kinetic functions and Kaehler metrics for some T6/Z(2)xZ(2) models with rigid D-branes of arXiv:0902.1694 [hep-th] by Angelantonj et al. As a second class of examples, the Kaehler metrics and gauge kinetic functions for the fractional QCD and leptonic D6-brane stacks of the Standard Model on T6/Z(6') from arXiv:0806.3039 [hep-th] by Gmeiner and Honecker are given.
We give a complete classification of T6/[Z(2)xZ(2M)xOmegaR] orientifolds on factorisable tori and rigid D6-branes on them. The analysis includes the supersymmetry, RR tadpole cancellation and K-theory conditions and complete massless open and closed string spectrum (i.e. non-chiral as well as chiral) for fractional or rigid D6-branes for all inequivalent compactification lattices, without and with discrete torsion. We give examples for each orbifold background, which show that on Z(2)xZ(6) and Z(2)xZ(6') there exist completely rigid D6-branes despite the self-intersections of orbifold image cycles. This opens up a new avenue for improved Standard Model building. On the other hand, we show that Standard and GUT model building on the Z(2)xZ(4) background is ruled out by simple arguments.
We perform a complete analysis of one-loop threshold corrections to the gauge couplings of fractional D6-branes. This includes besides SU(N) also symplectic, orthogonal and massless Abelian gauge factors and the full computation of contributions from discrete and continuous Wilson lines and brane displacements. Two classes of globally consistent supersymmetric compactifications with Standard Model spectra on T6/Z6 and T6/Z6' are presented in detail with the latter exhibiting the potential of supersymmetry breaking via a hidden sector gaugino condensate. The T6/Z6' Standard Models are completely classified, and it turns out that out of 768 distinct D6-brane configurations only 16 different sets of massless spectra and ten distinct values of gauge couplings at one-loop arise. The gauge threshold corrections enhance the diversity to 196 nonequivalent models.
Using previous results on the statistics of intersecting D6-brane models on T^6/Z_6' we analyse solutions that resemble the gauge group and matter content of the supersymmetric standard model. In particular the structure of the hidden sector, the gauge coupling constants and chiral exotic matter content are computed and classified for all possible standard model-like configurations on this background. It turns out that the number of chiral exotics, Higgses and values of gauge couplings are strongly correlated. Some examples with the chiral spectrum of the supersymmetric standard model plus vector-like states and a massless U(1) B-L are discussed in detail.
Following the recent exploration of smooth heterotic compactifications with unitary bundles, orbifold compactifications in six dimensions can be shown to correspond in the blow-up to compactifications with U(1) gauge backgrounds. A powerful tool is the comparison of anomaly polynomials. The presentation here focuses on heterotic SO(32) compactifications in six dimensions including five-branes. Four dimensional and E8 x E8 models are briefly commented on.
We provide a complete classification and statistical analysis of all type IIA orientifold compactifications with intersecting D6-branes on the orbifold T^6/Z'_6. The total number of four dimensional N=1 supersymmetric models is found to be O(10^23). After a statistical analysis of the gauge sector properties of all possible solutions, we study three subsets of configurations which contain the chiral matter sector of the standard model, a Pati-Salam or SU(5) GUT model, respectively. We find O(10^15) compactifications with an MSSM and O(10^11) models with a Pati-Salam sector. Along the way we derive an explicit algebraic formulation for the computation of the non-chiral matter spectrum for all Z_N orbifolds.
We clarify the relation between six-dimensional Abelian orbifold compactifications of the heterotic string and smooth heterotic K3 compactifications with line bundles for both SO(32) and E_8 x E_8 gauge groups. The T^4/Z_N cases for N=2,3,4 are treated exhaustively, and for N=6 some examples are given. While all T^4/Z_2 and nearly all T^4/Z_3 models have a simple smooth match involving one line bundle only, this is only true for some T^4/Z_4 and T^4/Z_6 cases. We comment on possible matchings with more than one line bundle for the remaining cases. The matching is provided by comparisons of the massless spectra and their anomalies as well as a field theoretic analysis of the blow-ups.
We systematically consider heterotic SO(32) and E8 x E8 compactifications on K3 with Abelian and non-Abelian backgrounds as well as an arbitrary number of five-branes. The masses of the U(1) factors depend on the first Chern classes of the bundles and some combinatorial factors specifying the embedding in SO(32) or E8. The form of the generalised Green-Schwarz counter-terms in six dimensions constrains the possible heterotic five-brane actions. Some supersymmetric examples on K3 realisations as toric complete intersection spaces with up to three explicit two-forms are given.
Continuing our recent work hep-th/0411173, we study the statistics of four-dimensional, supersymmetric intersecting D-brane models in a toroidal orientifold background. We have performed a vast computer survey of solutions to the stringy consistency conditions and present their statistical implications with special emphasis on the frequency of Standard Model features. Among the topics we discuss are the implications of the K-theory constraints, statistical correlations among physical quantities and an investigation of the various statistical suppression factors arising once certain Standard Model features are required. We estimate the frequency of an MSSM like gauge group with three generations to be one in a billion.
We extend the string model building rules for the construction of chiral supersymmetric Type I compactifications on smooth Calabi-Yau manifolds. These models contain stacks of D9-branes endowed with general stable U(n) bundles on their world-volume and D5-branes wrapping holomorphic curves on the Calabi-Yau.
We discuss chiral supersymmetric compactifications of the SO(32) heterotic string on Calabi-Yau manifolds equipped with direct sums of stable bundles with structure group U(n). In addition we allow for non-perturbative heterotic five-branes. These models are S-dual to Type I compactifications with D9- and D5-branes, which by themselves are mirror symmetric to general intersecting D6-brane models. For the construction of concrete examples we consider elliptically fibered Calabi-Yau manifolds with SU(n) bundles given by the spectral cover construction. The U(n) bundles are obtained via twisting by line bundles. We present a four-generation Pati-Salam and a three-generation Standard-like model.
We discuss perturbative four-dimensional compactifications of both the SO(32) heterotic and the Type I string on smooth Calabi-Yau manifolds endowed with general non-abelian and abelian bundles. We analyse the generalized Green-Schwarz mechanism for multiple anomalous U(1) factors and derive the generically non-universal one-loop threshold corrections to the gauge kinetic function as well as the one-loop corrected Fayet-Iliopoulos terms. The latter can be interpreted as a stringy one-loop correction to the Donaldson-Uhlenbeck-Yau condition. Applying S-duality, for the Type I string we obtain the perturbative Pi-stability condition for non-abelian bundles on curved spaces. Some simple examples are given, and we qualitatively discuss some generic phenomenological aspects of this kind of string vacua. In particular, we point out that in principle an intermediate string scale scenario with TeV scale large extra dimensions might be possible for the heterotic string.
We consider the E8 x E8 heterotic string theory compactified on Calabi-Yau manifolds with bundles containing abelian factors in their structure group. Generic low energy consequences such as the generalised Green-Schwarz mechanism for the multiple anomalous abelian gauge groups are studied. We also compute the holomorphic gauge couplings and induced Fayet-Iliopoulos terms up to one-loop order, where the latter are interpreted as stringy one-loop corrections to the Donaldson-Uhlenbeck-Yau condition. Such models generically have frozen combinations of Kaehler and dilaton moduli. We study concrete bundles with structure group SU(N) x U(1)^M yielding quasi-realistic gauge groups with chiral matter given by certain bundle cohomology classes. We also provide a number of explicit tadpole free examples of bundles defined by exact sequences of sums of line bundles over complete intersection Calabi-Yau spaces. This includes one example with precisely the Standard Model gauge symmetry.
In this paper, globally N=1 supersymmetric configurations of intersecting D6-branes on the Z6-orientifold are discussed, involving also fractional branes. It turns out rather miraculously that one is led almost automatically to just ONE particular class of 5 stack models containing the SM gauge group, which all have the same chiral spectrum. The further discussion shows that these models can be understood as exactly the supersymmetric standard model without any exotic chiral symmetric/antisymmetric matter. The superpartner of the Higgs finds a natural explanation and the hypercharge remains massless. However, the non-chiral spectrum within the model class is very different and does not in all cases allow for a N=2 low energy field theoretical understanding of the necessary breaking U(1)xU(1)->U(1) along the Higgs branch, which is needed in order to get the standard Yukawa couplings. Also the left-right symmetric models belong to exactly one class of chiral spectra, where the two kinds of exotic chiral fields can have the interpretation of forming a composite Higgs. The aesthetical beauty of these models, involving only non-vanishing intersection numbers of an absolute value three, seems to be unescapable.
We investigate the statistics of the phenomenologically important D-brane sector of string compactifications. In particular for the class of intersecting D-brane models, we generalise methods known from number theory to determine the asymptotic statistical distribution of solutions to the tadpole cancellation conditions. Our approach allows us to compute the statistical distribution of gauge theoretic observables like the rank of the gauge group, the number of chiral generations or the probability of an SU(N) gauge factor. Concretely, we study the statistics of intersecting branes on T^2 and T^4/Z_2 and T^6/Z_2 x Z_2 orientifolds. Intriguingly, we find a statistical correlation between the rank of the gauge group and the number of chiral generations. Finally, we combine the statistics of the gauge theory sector with the statistics of the flux sector and study how distributions of gauge theoretic quantities are affected.
D6-branes intersecting at angles allow for phenomenologically appealing constructions of four dimensional string theory vacua. While it is straightforward to obtain non-supersymmetric realizations of the standard model, supersymmetric and stable models with three generations and no exotic chiral matter require more involved orbifold constructions. The T^6/(Z_4 x Z_2 x OmegaR) case is discussed in detail. Other orbifolds including fractional D6-branes are treated briefly.
Intersecting D-brane worlds provide phenomenologically appealing constructions of four dimensional low energy string vacua. In this talk, a Z_4 x Z_2 orbifold background is taken into account. It is possible to obtain supersymmetric and stable chiral models. In particular, a three generation model with Pati-Salam gauge group and no exotic chiral matter is presented.