**Background**

Despite its great success, the Standard Model (SM) of particle physics cannot be the ultimate theory describing elementary particles and their interactions. The conflict between quantum mechanics and general relativity as well as recent data from cosmology and astrophysics show the need for a new fundamental theory of space-time, matter and forces. At present, the most promising candidate is String Theory.

In order to have any hope of testing String Theory one needs first to understand its effective theories, as these are directly related to the physics that can be seen in the laboratories. This is especially important in the next few years because the Large Hadron Collider (LHC) is going to deliver its first results on particle interactions at the TeV scale and reveal signals of any new physics beyond the SM.

In this framework, a prominent role is played by supergravity theories, which can provide low-energy approximations to String Theory. Especially important, for their phenomenological applications, is the analysis of the allowed couplings, masses and of spontaneous SUSY breaking patterns, the ultimate hope of this analysis being the selection of the right vacuum for phenomenological applications. Although this process is going to produce many four-dimensional vacua that are unsuitable for phenomenology, the same vacua can, however, be holographically dual to three-dimensional field theories and are hence of independent physical interest.

**Objectives**

This project aims at confronting some of the key issues related to the physics beyond the standard model among 3 main lines:

- Structure of 4-dimensional supergravity theories;
- String vacua and geometry of extra dimensions;
- Holography for 3-dimensional field theories.

1. We plan to complete the classification and construction of 4-dimensional gauged supergravities by generalizing the embedding tensor formalism. We aim to create a complete map for the landscape of different models clarifying which ones have a real and direct relation to string theory. For these, we also plan to work out the dictionary between 4- and 10-dimensional quantities, providing a stringy interpretation of 4-dimensional physics.

2. New geometrical methods (such as "generalized complex geometry"), reveal many possible new classes of string vacua, whose physical features look very different from the ones known so far. We propose to find and classify these new vacua, and to use them to construct new mechanisms to solve some of the challenges of string phenomenology, such as moduli stabilization and controlled SUSY breaking.

3. Recent progress in holography allows to write explicit conformal field theory duals to four-dimensional string vacua. This can be used to predict new vacua using field theory, as well as to new spinoffs in the physics of materials which effectively extend along two space dimensions, such as graphene, some superconductors, and systems with non-relativistic symmetries.