Gerardo Aldazabal

D-Branes at Singularities : A Bottom-Up Approach to the String Embedding of the Standard Model

We propose a bottom-up approach to the building of particle physics models from string theory. Our building blocks are Type II D-branes which we combine appropriately to reproduce desirable features of a particle theory model: 1) Chirality ; 2) Standard Model group ; 3) N =1 orN = 0 supersymmetry ; 4) Three quark-lepton generations. We start such a program by studying congurations of D = 10, Type IIB D3-branes located at singularities. We study in detail the case of ZZN N =1 ; 0 orbifold singularities leading to the SM group or some left-right symmetric extension. In general, tadpole cancellation conditions require the presence of additional branes, e.g. D7-branes. For the N =1s upersymmetric case the unique twist leading to three quark-lepton generations is ZZ3, predicting sin 2 W =3 =14 = 0:21. The models obtained are the simplest semirealistic string models ever built. In the non-supersymmetric case there is a three-generation model for each ZZN, N> 4, but the Weinberg angle is in general too small. One can obtain a large class of D =4 compact models by considering the above structure embedded into a Calabi Yau compactication. We explicitly construct examples of such compact models using ZZ3 toroidal orbifolds and orientifolds, and discuss their properties. In these examples, global cancellation of RR charge may be achieved by adding anti-branes stuck at the xed points, leading to models with hidden sector gravity-induced supersymmetry breaking. More general frameworks, like F-theory compactications, allow completely N = 1 supersymmetric embeddings of our local structures, as we show in an explicit example.

D = 4 chiral string compactifications from intersecting branes

Intersecting Dp-branes often give rise to chiral fermions living on their intersections. We study the construction of four-dimensional chiral gauge theories by considering configurations of type II D(3+n)-branes wrapped on nontrivial n-cycles on T2n×(R2(3−n)/ZN), for n=1, 2, 3. The gauge theories on the four noncompact dimensions of the brane world-volume are generically chiral and nonsupersymmetric. We analyze consistency conditions (RR tadpole cancellation) for these models, and their relation to four-dimensional anomaly cancellation. Cancellation of U(1) gauge anomalies involves a Green–Schwarz mechanism mediated by RR partners of untwisted and/or twisted moduli. This class of models is of potential phenomenological interest, and we construct explicit examples of SU(3)×SU(2)×U(1) three-generation models. The models are nonsupersymmetric, but the string scale may be lowered close to the weak scale so that the standard hierarchy problem is avoided. We also comment on the presence of scalar tachyons and p...

Double field theory: a pedagogical review

Double field theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical presentation of DFT and its applications. We first introduce some basic ideas on T-duality and supergravity in order to proceed to the construction of generalized diffeomorphisms and an invariant action on the double space. Steps towards the construction of a geometry on the double space are discussed. We then address generalized Scherk–Schwarz compactifications of DFT and their connection to gauged supergravity and flux compactifications. We also discuss U-duality extensions and present a brief parcours on worldsheet approaches to DFT. Finally, we provide a summary of other developments and applications that are not discussed in detail in the review.

The effective action of Double Field Theory

A bstractWe perform a generalized Scherk-Schwarz dimensional reduction of Double Field Theory on a twisted double torus. The four dimensional effective action is shown to exactly reproduce the bosonic electric sector of gauged

D = 4, N=1, type IIB orientifolds

\mathcal{N}

More dual fluxes and moduli fixing

 = 4 supergravity. We present explicit expressions for the gaugings in terms of the twists, and analyze the associated string backgrounds. This framework provides a higher dimensional origin of the gaugings in terms of generalized fluxes.

Standard - like models with broken supersymmetry from type I string vacua

We study different aspects of the construction of D = 4, N = 1 type IIB orientifolds based on toroidal ZN and ZM × ZN, D = 4 ortifolds. We find that tadpole cancellation conditions are in general more constraining than in six dimensions and that the standard Gimon-Polchinski orientifold projection leads to the impossibility of tadpole cancellations in a number of ZN orientifolds with even N including Z4, Z8, Z8′ and Z12′. We construct D = 4, ZN and ZN × ZM orientifolds with different configurations of 9-branes, 5-branes and 7-branes, most of them chiral. Models including the analogue of discrete torsion are constructed and shown to have features previously conjectured on the basis of F-theory compactified on four-folds. Different properties of the D = 4, N = 1 models obtained are discussed including their possible heterotic duals and effective low-energy action. These models have in general more than one anomalous U(1) and the anomalies are cancelled by a D = 4 generalized Green-Schwarz mechanism involving dilaton and moduli fields.

Extended geometry and gauged maximal supergravity

We generalize the recent proposal that invariance under T-duality leads to additional non-geometric fluxes required so that superpotentials in type IIA and type IIB orientifolds match. We show that invariance under type IIB S-duality requires the introduction of a new set of fluxes leading to further superpotential terms. We find new classes of = 1 supersymmetric Minkowski vacua based on type IIB toroidal orientifolds in which not only dilaton and complex moduli but also K?hler moduli are fixed. The chains of dualities relating type II orientifolds to heterotic and M-theory compactifications suggests the existence of yet further flux degrees of freedom. Restricting to a particular type IIA/IIB or heterotic compactification only some of these degrees of freedom have a simple perturbative and/or geometric interpretation.

A

We construct D = 4 Type I vacua with massless content remarkably close to that of the standard model of particle physics. They are tachyon-free nonsupersymmetric models which are obtained starting with a standard D =4 , N= 1 compact Type IIB orientifold and adding the same number of Dp-branes and anti-Dp-branes distributed at dierent points of the underlying orbifold. Supersymmetry-breaking is felt by the observable world either directly, by gravity mediation or gauge mediation, depending on the brane conguration. We construct several simple three generation examples with the gauge group of the standard model or its left-right symmetric extensions. The models contain a number of U(1) gauge groups whose anomalies are cancelled by a generalized Green-Schwarz mechanism. These U(1)’s are broken but may survive as global symmetries providing for a flavour structure to the models. The value of the string scale may be lowered down to the intermediate scale (as required in the gravity mediation case) or down to 1-100 TeV for the non-SUSY models. Thus the present models are the rst semirealistic string vacua realizing the possibility of a low string scale. The unbalanced force between the pairs of Dp- and anti-Dp-branes provides for an eect which tends to compactify some of the extra dimensions but no others. This could provide a new mechanism for radius stabilization.

D^-

A bstractWe consider generalized diffeomorphisms on an extended mega-space associated to the U-duality group of gauged maximal supergravity in four dimensions, E7(7). Through the bein for the extended metric we derive dynamical (field-dependent) fluxes taking values in the representations allowed by supersymmetry, and obtain their quadratic constraints from gauge consistency conditions. A covariant generalized Ricci tensor is introduced, defined in terms of a connection for the generalized diffeomorphisms. We show that for any torsionless and metric-compatible generalized connection, the Ricci scalar reproduces the scalar potential of gauged maximal supergravity. We comment on how these results extend to other groups and dimensions.