NAC PHENO · Deformed geometry and phenomenology

Final Activity Report Summary - NAC PHENO (Deformed geometry and phenomenology.)

The fundamental aim in physics is to explain different phenomena in terms of the same mathematical structures. From this point of view, after centuries of experimental research and theoretical studies, we could say that we have, at present, a quite satisfactory picture of our universe. Everything, from the very small to the very big scale, seems to be built by known interacting elementary particles. These interactions are characterised by the four elementary forces, i.e. electromagnetism, gravity, weak and strong forces. Moreover, there is already evidence that electromagnetism and the weak force are actually a single force, and this is explained by the standard model of particle physics. The reason why we are able to describe in a unique way things so different is translated in physics by saying that there is an underlying ‘symmetry’. The details of a given symmetry can give us the characteristics of the particles and the involved forces. The trend is currently towards symmetries that relate ever more disparate phenomena. These symmetries tend to contain many novel elements. The existence of previously unknown particles, that were later seen in experiments has been, in fact, predicted as missing elements of nearly symmetric systems. In the same spirit, but from the opposite point of view, little incongruences from theoretical predictions and experimental data could be interpreted by the lack of some ingredients in the model. This is indeed what happens now in particle physics. The standard model is in nearly agreement with observations, but small signals suggest that we are missing something. The so-called ‘beyond the standard model’ theories are thus based on different applications of the same idea. The most promising one postulates a new symmetry between the particles that constitute matter and those carrying the interactions, which is known as supersymmetry (SUSY). Going just one step beyond, we can include gravity, the so-called supergravity, and introduce extra-dimensions. Or still, we can combine all these ideas and study string theory. In all these cases, the standard model has to be recovered in the appropriate limit. The aim of my research project was therefore to study the connections between the experimental data and the theoretical extensions of the standard model, in particular the string theory inspired ones, and the models which were their effective realisations at energy scales close to those explored by the large hadron collider (LHC) in the very near future. There were different aspects that one had to check in constructing such phenomenological models. For example, SUSY had to be broken in a correct way, in agreement with the present experimental data. At the same time, not all these possibilities were compatible from a formal point of view and first principles. As such, we investigated during my fellowship the formal properties of field theories for which SUSY was partially broken via a particular mechanism related to a deformation of the geometry of the space and time where they were embedded. These non-(anti)commutative N=1/2 SUSY theories conserved very nice features of the original unbroken SUSY field theories. In particular, we stressed out that gauge theories, i.e. the most important ones from a phenomenological point of view, remained renormalisable after these deformations and we also analysed their quantum properties in cases with different contents in matter. Moreover, we studied models in supergravity setup, trying to establish the conditions under which gauge mediation was a good candidate as a SUSY breaking mechanism. In this framework we found that it was difficult to obtain this phenomenologically interesting construction in a natural way when string theoretical constraints were imposed, like the stabilisation of the light modes. In particular, we had to take into account the interplay with contributions coming from the gravitational sector and other specific phenomena of scenarios with extra anomalous abelian gauge interactions.

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