This thesis concerns a range of aspects of theoretical physics. It is composed of two parts. In the first part we motivate our line of research, and introduce and discuss the relevant concepts. In the second part, four research papers are collected. The first paper deals with a possible extension of general relativity, namely the recently discovered classically consistent bimetric theory. In this paper we study the behavior of perturbations of the metric(s) around cosmologically viable background solutions. In the second paper, we explore possibilities for particle physics with low-scale supersymmetry. In particular we consider the addition of supersymmetric higher-dimensional operators to the minimal supersymmetric standard model, and study collider phenomenology in this class of models. The third paper deals with a possible extension of the notion of Lie algebras within category theory. Considering Lie algebras as objects in additive symmetric ribbon categories we define the proper Killing form morphism and explore its role towards a structure theory of Lie algebras in this setting. Finally, the last paper is concerned with the computation of string amplitudes in four dimensional models with reduced supersymmetry. In particular, we develop general techniques to compute amplitudes involving gauge bosons and gravitons and explicitly compute the corresponding three- and four-point functions. On the one hand, these results can be used to extract important pieces of the effective actions that string theory dictates, on the other they can be used as a tool to compute the corresponding field theory amplitudes. / Over the last twenty years there have been spectacular observations and experimental achievements in fundamental physics. Nevertheless all the physical phenomena observed so far can still be explained in terms of two old models, namely the Standard Model of particle physics and the ΛCDM cosmological model. These models are based on profoundly different theories, quantum field theory and the general theory of relativity. There are many reasons to believe that the SM and the ΛCDM are effective models, that is they are valid at the energy scales probed so far but need to be extended and generalized to account of phenomena at higher energies. There are several proposals to extend these models and one promising theory that unifies all the fundamental interactions of nature: string theory. With the research documented in this thesis we contribute with four tiny drops to the filling of the fundamental physics research pot. When the pot will be saturated, the next fundamental discovery will take place.

Une théorie des champs quantique topologique (TQFT) en dimension 3 est un foncteur monoidal symétrique de la catégorie des cobordismes de dimension 3 vers celle des espaces vectoriels. Une TQFT fournit en particulier un invariant scalaire des variétés fermées de dimension 3 ainsi que des représentations du groupe de difféotopie des surfaces fermées.Turaev explique en 1994 comment construire à partir d'une catégorie modulaire une TQFT qui étend l'invariant scalaire de 3-variétés fermées introduit en 1991 par Reshetikhin et Turaev. Dans cette thèse, nous généralisons cette construction à l'aide d'une catégorie C en ruban avec coend. On représente un cobordisme par un enchevêtrement d'un type particulier (enchevêtrement de cobordisme) et on associe à celui-ci un morphisme défini entre puissances tensorielles de la coend comme décrit par Lyubashenko en 1995. A l'aide de l'extension du calcul de Kirby aux cobordismes de dimension 3, cette construction nous permet de produire un invariant de cobordismes puis une TQFT à valeurs dans la sous-catégorie monoïdale symétrique des objets transparents de C.Dans le cas où C est une catégorie modulaire, cette sous-catégorie s'identifie à celle des espaces vectoriels et on retrouve ainsi la TQFT de Turaev. Dans le cas où C est une catégorie prémodulaire modularisable, notre TQFT est un relèvement de la TQFT de Turaev associée à la modularisée de C. / A 3-dimensional topological quantum field theory (TQFT) is a symmetric monoidal functor from the category of 3-cobordisms to the category of vector spaces. Such TQFTs provide in particular numerical invariants of closed 3-manifolds and representations of the mapping class group of closed surfaces.In 1994, Turaev explains how to construct a TQFT from a modular category; the scalar invariant is then the Reshethikhin-Turaev invariant introduced in 1991. In this thesis, we describe a generalization of this construction starting from a ribbon category C with coend. We present a cobordism by a certain type of tangle (cobordism tangle) and we associate to such a tangle a morphism between tensor products of the coend as described by Lyubashenko in 1994. Extending the Kirby calculus to 3-cobordisms, we obtain in this way an invariant of cobordisms and a TQFT which takes values in the symmetric monoidal subcategory of transparent objects of C. If the category C is modular, this subcategory can be identified with the category of vector spaces, and we recover Turaev's TQFT. If the category C is modularizable, our TQFT is a lift of the Turaev TQFT for the modularization of C.