### String theory

String Theory has been for more than two decades, and still is, the only candidate for a theory of the elementary particles and their interactions, that includes gravity. This theory proposes that elementary particles are tiny one-dimensional strings instead of point particles, as stated in Quantum Field Theory. String Theory actually predicts the existence of gravity since it is not possible to construct any of these theories without the presence of gravitons. String Theory is therefore a very strong candidate for a theory of Quantum Gravity too. Other important features of String Theory is that the gauge groups and the representations resulting from these theories, are fixed for consistency, not put by hand unlike in Quantum Field Theory. In 2005 it was realized that String Theory contains also branes, which are the objects to which the ends of the open strings are attached and are very important for consistency. Other important quasi-predictions, of String Theory are the existence of extra spatial dimensions and the existence of Supersymmetry. That is, most string models one can construct contain extra space dimensions and/or supersymmetry. These two features are currently searched for in the Large Hadron Collider (LHC) at CERN, together with the Higgs particle, in the new era of experiments in High Energy Physics that started in November 2009. Another merit of String Theory is that it has enriched enormously Mathematical Physics during all these years and it seems that it will continue doing so.

The String Theory group in the IFF investigates some mathematical abstract features of these theories as well as much more phenomenological aspects. In the last years the group has been searching and constructing theories which are compatible with the Standard Model of Particle Physics, either supersymmetric or non supersymmetric. For this purpose we used the orientifold construction and the asymmetric heterotic string construction both realized on Gepner models (tensor products of N=2 superconformal models), as well as some other constructions, like free fermion realizations. We found that realistic non supersymmetric strings on orientifold constructions tend to be problematic (either existence of tachyons or non-vanishing tadpoles) in the general case, or they have a supersymmetric massless spectrum of particles when they are not problematic. In the case of the asymmetric heterotic strings we invented a procedure, called lifting, that improves enormously the chances to find realistic models with the three families of fermions of the Standard Model.

However, to find realistic models is not the unique task in string model building. It turns out that each and every string model one can construct is interesting by itself because it could correspond to the physical laws of another universe, if we adopt the viewpoint of the Multiverse. As a matter of fact, at present and for the next two or three years, we intend to investigate various problems related to String Theory and to the Multiverse. The huge number of solutions of String Theory, dubbed the “String Theory Landscape", points towards the existence of the Multiverse in a very natural way, and the Multiverse, in its turn, provides the appropriate context where the String Theory Landscape can become a physical reality. In addition, in the framework of the New Standard Cosmology, Quantum Gravity and String Theory, this project aims at investigating several observable aspects that other universes may have induced or are actually inducing now in our own accelerating universe as well. That is, we will study the possibility of observable signatures left by primordial or non-primordial collisions.

B. Gato-Rivera and A.N. Schellekens, Nucl. Phys. B846, 429-468 (2011).

B-L Lifting, B. Gato-Rivera and A.N. Schellekens, Nucl. Phys. B847, 532-548 (2011).

B. Gato-Rivera and A.N. Schellekens, Nucl. Phys. B828, 375-389 (2010).

B. Gato-Rivera and A.N. Schellekens, Nucl. Phys. B841, 100-129 (2010).

#### Participants

B. Gato-Rivera, A. N. Schelleken”

### Homogeneous quaternionic Kaehler structures and target spaces of σ-models in N=2 supergravity

Since the works by Bagger and Witten, Cecotti, de Wit and van Proeyen, it is known and has been studied the target spaces of sugma-models in N=2 supergravity as quaternion-Kaehler manifolds of negative scalar curvature, the known spaces are those in Alekseevsky's, Cortes's and de Wit and van Proeyen's classification. They include symmetric spaces and non-symmetric ones, in the three T-, W-, and V-series found by Alekseevsky. On the other hand, Fino gave the classification in theoretical-representation terms of quaternionic-Kahler structures into five classes, and members of our team then the classification by real tensors. This classification permit us to conjecture that there is a corresponding classification of spaces, and this is one of the lines of research of our team. As a first step one should know what types of quaternionic Kaehler structures exist on the different classes of spaces. This was done for some kinds of quaternion-Kaehler symmetric spaces in previous papers and continued in the more recent papers cited below. Moreover, in the second paper a characterisation is given of a complex analogue of singular homogeneous plane waves in the Lorentzian case.

W. Batat, P. M. Gadea and J. A. Oubina, Homogeneous quaternionic Kaehler structures on rank-three Alekseevsky, Publ. Math. Debrecen 78 (2011), no. 3-4, 691-707.

W. Batat, P. M. Gadea and J. A. Oubina, Homogeneous pseudo-Riemannian structures of linear type, J. Geom. Phys. 61 (2011), no. 3, 745-764.

#### Participants

P. Martinez-Gadea