## Final Report Summary - STRING PHENO (Phenomenology of strings: generalized structures, non-perturbative physics and supersymmetry breaking)

The Standard Model (SM) of high energy physics provides a unifying framework for the strong, weak and electromagnetic interactions in nature. Despite the success of the SM at accelerator experiments, there are some fundamental aspects that miss a convincing theoretical description. Among these are the exclusion of the gravitational interaction from this unifying context, the flavour structure, the hierarchy problem or cosmological aspects such as the cosmological constant or the accelerated expansion. All of them seem to point out to some new physics beyond the SM.

String theory is one of the most promising candidates that we have to describe all particles and interactions in nature in a unified framework. Its main predictions are the existence of gravity, gauge interactions and supersymmetry in a consistent framework. These are the basic pillars of the SM, General relativity and much of the physics beyond the SM proposed up to now. A complete characterisation of the low energy physics of String theory is therefore of extreme importance, specially keeping in mind the Large Hadron Collider (LHC) facility which has started running this year, looking for experimental evidence of new physics.

This project intends to explore systematically some of the open questions in the characterisation of the low energy physics of String theory compactifications, with particular emphasis in the mechanisms for supersymmetry breaking and moduli stabilisation. The effective physics associated to a String theory compactification is generically thought to be given by:

1. A four dimensional gauged supergravity with classical flat directions in the scalar potential.

2. String and non-perturbative corrections to the above supergravity. These are especially important along the classical flat directions.

3. Gravitational redshift effects (warp effects), due to the backreaction of the sources.

The research activity carried out during this period mainly deals with points 1 and 2. In particular,

a) we have constructed non-supersymmetric no-scale deformations of SU(3)-structure compactifications, based on toroidal orbifolds with intrinsic torsion, both for type IIA and type I String theory. The conditions that the background have to satisfy in order to be a solution of the supergravity equations of motion have been clearly stated and the resulting patterns of soft supersymmetry breaking have been analysed. We find two types of solutions, depending whether the supersymmetry breaking is mediated exclusively by hypermultiplets or by a mixture of hypermultiplets and vector multiplets, the latter case corresponding to a class of Scherk-Schwarz compactifications.

b) we have computed and analysed the structure of non-perturbative corrections in toroidal orbifold compactifications. These are encoded in corrections to the Kahler potential, the gauge kinetic function and the superpotential. In particular, we have shown that the use of dualities, such as S-duality, constitute a powerful tool. Making use of this, we have computed in concrete models corrections, revealing an intricate structure of multi-instanton effects. These effects may play an active role in the stabilisation of the compactification scalars.

c) We have explored the 4d gauged supergravities resulting from general toroidal orbifold compactifications with magnetized D-branes, closed string fluxes and non-geometric fluxes (global monodromies for the axion-dilaton). Our results reveal that the 4d gauge algebra encodes much of the information on the higher dimensional String theory. Global consistency conditions, such as Bianchi identities, tadpole and Freed-Witten anomaly cancellation conditions, are encoded in the Jacobi identities of the 4d algebra. Moreover, we have developed techniques to compute the classical part of physical observables in these compactifications.

String theory is one of the most promising candidates that we have to describe all particles and interactions in nature in a unified framework. Its main predictions are the existence of gravity, gauge interactions and supersymmetry in a consistent framework. These are the basic pillars of the SM, General relativity and much of the physics beyond the SM proposed up to now. A complete characterisation of the low energy physics of String theory is therefore of extreme importance, specially keeping in mind the Large Hadron Collider (LHC) facility which has started running this year, looking for experimental evidence of new physics.

This project intends to explore systematically some of the open questions in the characterisation of the low energy physics of String theory compactifications, with particular emphasis in the mechanisms for supersymmetry breaking and moduli stabilisation. The effective physics associated to a String theory compactification is generically thought to be given by:

1. A four dimensional gauged supergravity with classical flat directions in the scalar potential.

2. String and non-perturbative corrections to the above supergravity. These are especially important along the classical flat directions.

3. Gravitational redshift effects (warp effects), due to the backreaction of the sources.

The research activity carried out during this period mainly deals with points 1 and 2. In particular,

a) we have constructed non-supersymmetric no-scale deformations of SU(3)-structure compactifications, based on toroidal orbifolds with intrinsic torsion, both for type IIA and type I String theory. The conditions that the background have to satisfy in order to be a solution of the supergravity equations of motion have been clearly stated and the resulting patterns of soft supersymmetry breaking have been analysed. We find two types of solutions, depending whether the supersymmetry breaking is mediated exclusively by hypermultiplets or by a mixture of hypermultiplets and vector multiplets, the latter case corresponding to a class of Scherk-Schwarz compactifications.

b) we have computed and analysed the structure of non-perturbative corrections in toroidal orbifold compactifications. These are encoded in corrections to the Kahler potential, the gauge kinetic function and the superpotential. In particular, we have shown that the use of dualities, such as S-duality, constitute a powerful tool. Making use of this, we have computed in concrete models corrections, revealing an intricate structure of multi-instanton effects. These effects may play an active role in the stabilisation of the compactification scalars.

c) We have explored the 4d gauged supergravities resulting from general toroidal orbifold compactifications with magnetized D-branes, closed string fluxes and non-geometric fluxes (global monodromies for the axion-dilaton). Our results reveal that the 4d gauge algebra encodes much of the information on the higher dimensional String theory. Global consistency conditions, such as Bianchi identities, tadpole and Freed-Witten anomaly cancellation conditions, are encoded in the Jacobi identities of the 4d algebra. Moreover, we have developed techniques to compute the classical part of physical observables in these compactifications.