Dr Eran Palti

String theory is as simple as it sounds: it is the theory describing a string subject to the principles of quantum mechanics. It is an amazing thing that in constructing such a theory one is forced to introduce gravity, supersymmetry and predict the number of space-time dimensions. No less remarkable is that the fundamental build blocks of the Standard Model of particle physics: gauge symmetries, chiral fermions, scalar fields, all arise naturally and sometimes inevitably out of the theory. This makes the theory of strings so rich that it is able to shed light on nearly all aspects of fundamental physics. The particular aspect that I primarily work on is how do the particles and interactions that we observe in nature arise from the theory, what can it teach us about why they have the properties that they do and what else can we expect to find.

One of the topics I work on is building Grand Unified Theories (GUTs) in F-theory. GUTs are theories where the three forces of the Standard Model unify into a single force at a high energy scale; the GUT scale. We have good reasons to believe this should be the case because the experimentally measured couplings of the Weak, Strong and Electromagnetic forces do unify at a high scale. F-theory refers to (type IIB) string theory but in a regime where the self coupling of the string is strong, so perturbative string theory breaks down. In F-theory (analogously to M-theory) aspects of string theory, in particular the string coupling and 7-branes are geometrised: overall we consider 8 extra dimensions, but only 6 are physical, the other two, which are in the shape of a torus, describe the string coupling and 7-branes.

The way in which the additional torus of F-theory describes 7-branes is an active area of research. This is important because the forces and particles of our universe arise on intersecting 7-branes in F-theory. We are learning how familiar aspects of particle physics, such as gauge symmetries and chiral matter, correspond to various geometric properties of the torus such as its width shrinking to zero at a point and forming two intersecting spheres. The way the torus geometry varies over the extra dimensions is called the elliptic fibration, and I have been working on various aspects of it such as understanding Abelian gauge symmetries by constructing elliptic fibrations with multiple sections: each section describes an extra Abelian symmetry.

One of the greatest puzzles of the Standard Model of particle physics is why there are three copies, termed generations or flavours, of each type of particle? And why the three generations share exactly the same properties with regards to the Standard Model forces, but have widely varying masses: for example the top quark is a hundred thousand times heavier than the up quark. I have worked on models coming from string theory which provide a rather natural explanations for the very different masses of the three generations (and also why they do not mix very much). The idea is to embed the Standard Model into a single field which transforms as an adjoint of the exceptional group E8. Such a field arises naturally in string theory, and with Emilian Dudas, I have shown that there is a unique embedding of the Standard Model particles into E8 which can recreate the observed masses and mixing of the quarks and leptons. Indeed this embedding can explain around 10 parameters of the Standard Model in terms of just two input parameters. It even made an experimental prediction that a certain neutrino mixing angle will be non-vanishing, and this was experimentally confirmed recently by the Daya-Bay experiment.

The Heterotic String is one of the phenomenologically realistic regions of string theory. As a collaboration with Lara Anderson, James Gray and Andre Lukas, we initiated a whole new approach to model building in this arena. We constructed particle physics models which come from reducing the Heterotic string on Calabi-Yau manifolds with Abelian fluxes only, this being in contrast to the non-Abelian fluxes that have been used in the 25 years of Heterotic model building prior to our work. The new approach has proved very successful and we have constructed thousands of compactifications which lead to a massless spectrum which is exactly that of the supersymmetric Standard Model. We are now in the process of classifying all such possible models on certain Calabi-Yau manifolds, and studying their more detailed phenomenology such as the Yukawa couplings.

The shape of the extra dimensions of string theory is dynamic, their geometry can change and this variation corresponds to a four-dimensional scalar field: a modulus. In order to extract predictions from specific string theory models, and also to satisfy constraints on light scalar fields, we must find ways to fix the geometry which in terms of four-dimensional physics means giving all the moduli fields a mass. This process is called moduli stabilisation, and I have worked on ways to achieve this on manifolds which are not of Calabi-Yau type. One of the results I have found is that manifolds with torsion, such as cosets, generally allow all moduli to be fixed. String theory allows for yet more exotic possibilities for its extra dimensions: it could be that they are not even geometric in the sense of our current theory of gravity which is general relativity. Such spaces are called non-geometric compactifications and one of the areas I have worked on is moduli stabilisation on such spaces.