arXiv subjects
Publications and source records attributed to Ralph Blumenhagen.
The Affleck-Dine-Seiberg instanton generated superpotential for SQCD with Nf=Nc-1 flavours is explicitly derived from a local model of engineered intersecting D6-branes with a single E2-instanton. This computation extends also to symplectic gauge groups with Nf=Nc flavours.
We systematically investigate instanton corrections from wrapped Euclidean D-branes to the matter field superpotential of various classes of N=1 supersymmetric D-brane models in four dimensions. Both gauge invariance and the counting of fermionic zero modes provide strong constraints on the allowed non-perturbative superpotential couplings. We outline how the complete instanton computation boils down to the computation of open string disc diagrams for boundary changing operators multiplied by a one-loop vacuum diagram. For concreteness we focus on E2-instanton effects in Type IIA vacua with intersecting D6-branes, however the same structure emerges for Type IIB and heterotic vacua. The instantons wrapping rigid cycles can potentially destabilise the vacuum or generate perturbatively absent matter couplings such as proton decay operators, mu-parameter or right-handed neutrino Majorana mass terms. The latter allow the realization of the seesaw mechanism for MSSM-like intersecting D-brane models.
We provide the methods to compute the complete massless spectra of a class of recently introduced supersymmetric E8 x E8 heterotic string models which invoke vector bundles with U(N) structure group on simply connected Calabi-Yau manifolds and which yield flipped SU(5) and MSSM string vacua of potential phenomenological interest. We apply Leray spectral sequences in order to derive the localisation of the cohomology groups H^i(X,V_a \times V_b), H^i(X,\bigwedge^2 V) and H^i(X,{\bf S}^2 V) for vector bundles defined via Fourier-Mukai transforms on elliptically fibered Calabi-Yau manifolds. By the method of bundle extensions we define a stable U(4) vector bundle leading to the first flipped SU(5) model with just three generations, i.e. without any vector-like matter. Along the way, we propose the notion of Lambda-stability for heterotic bundles.
We consider four-dimensional supersymmetric compactifications of the E8 x E8 heterotic string on Calabi-Yau manifolds endowed with vector bundles with structure group SU(N) x U(1) and five-branes. After evaluating the Green-Schwarz mechanism and deriving the generalized Donaldson-Uhlenbeck-Yau condition including the five-brane moduli, we show that this construction can give rise to GUT models containing U(1) factors like flipped SU(5) or directly the Standard Model even on simply connected Calabi-Yau manifolds. Concrete realizations of three-generation models on elliptically fibered Calabi-Yau manifolds are presented. They exhibit the most attractive features of flipped SU(5) models such as doublet-triplet splitting and proton stability. In contrast to conventional GUT string models, the tree level relations among the Standard Model gauge couplings at the GUT scale are changed.
We investigate Z2 x Z2 orientifolds with group actions involving shifts. A complete classification of possible geometries is presented where also previous work by other authors is included in a unified framework from an intersecting D-brane perspective. In particular, we show that the additional shifts not only determine the topology of the orbifold but also independently the presence of orientifold planes. In the second part, we work out in detail a basis of homological three cycles on shift Z2 x Z2 orientifolds and construct all possible fractional D-branes including rigid ones. A Pati-Salam type model with no open-string moduli in the visible sector is presented.
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.
Most intersecting D-brane vacua in the literature contain additional massless adjoint fields in their low energy spectrum. The existence of these additional fields make it difficult to obtain negative beta functions and, eventually, asymptotic freedom. We address this important issue for N=1 intersecting D-brane models, rephrasing the problems in terms of (open string) moduli stabilization. In particular, we consider a Z2 x Z2 orientifold construction where D6-branes wrap rigid 3-cycles and such extra adjoint fields do not arise. We derive the model building rules and consistency conditions for intersecting branes in this background, and provide N=1 chiral vacua free of adjoint fields. More precisely, we construct a Pati-Salam-like model whose SU(4) gauge group is asymptotically free. We also comment on the application of these results for obtaining gaugino condensation in chiral D-brane models. Finally, we embed our constructions in the framework of flux compactification, and construct new classes of N=1 and N=0 chiral flux vacua.
We study supersymmetric intersecting D6-branes wrapping 3-cycles in the Type IIA T^6/Z_4 orientifold background. As a new feature, the 3-cycles in this orbifold space arise both from the untwisted and the Z_2 twisted sectors. We present an integral basis for the homology lattice, H_3(M,Z), in terms of fractional 3-cycles, for which the intersection form involves the Cartan matrix of E8. We show that these fractional D6-branes can be used to construct supersymmetric brane configurations realizing a three generation Pati-Salam model. Via brane recombination processes preserving supersymmetry, this GUT model can be broken down to a standard-like model.
We provide a pedagogical introduction to a recently studied class of phenomenologically interesting string models, known as Intersecting D-Brane Models. The gauge fields of the Standard-Model are localized on D-branes wrapping certain compact cycles on an underlying geometry, whose intersections can give rise to chiral fermions. We address the basic issues and also provide an overview of the recent activity in this field. This article is intended to serve non-experts with explanations of the fundamental aspects, and also to provide some orientation for both experts and non-experts in this active field of string phenomenology.
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.
The aim of this article is to review some recent progress in the field of intersecting D-brane models. This includes the construction of chiral, semi-realistic flux compactifications, the systematic study of Gepner model orientifolds, the computation of various terms in the low energy effective action and the investigation of the statistics of solutions to the tadpole cancellation conditions.
We construct Type IIA orientifolds for general supersymmetric Z_N orbifolds. In particular, we provide the methods to deal with the non-factorisable six-dimensional tori for the cases Z7, Z8, Z8', Z12 and Z12'. As an application of these methods we explicitly construct many new orientifold models.
In this note we generalize the description of simple current extended Gepner Model orientifolds as presented in hep-th/0401148 to the case of even levels and non-trivial dressings of the parity transformation. We provide a comprehensive list of all the important ingredients for the construction of such orientifolds. Namely we present explicit expressions for the Klein-bottle, annulus and Moebius strip amplitudes and derive the general tadpole cancellation conditions. As an example we construct a supersymmetric Pati-Salam like model.
We explicitly construct A-type orientifolds of supersymmetric Gepner models. In order to reduce the tadpole cancellation conditions to a treatable number we explicitly work out the generic form of the one-loop Klein bottle, annulus and Moebius strip amplitudes for simple current extensions of Gepner models. Equipped with these formulas, we discuss two examples in detail to provide evidence that in this setting certain features of the MSSM like unitary gauge groups with large enough rank, chirality and family replication can be achieved.