This thesis is devoted to various aspects of electric-magnetic duality and its gravitational generalization, with an emphasis on the case of maximal supergravity. It is divided into three parts.In the first part, we review the symmetries of maximal supergravity in various dimensions, with a particular focus on the exceptional ``hidden" symmetries that appear upon toroidal dimensional reduction of eleven-dimensional supergravity. Two new results are obtained. First, we prove in detail that these hidden symmetries appear if and only if the Chern-Simons coupling of the eleven-dimensional theory takes the value predicted by supersymmetry. Second, we obtain a manifestly E7(7)-invariant formula for the entropy of non-extremal black holes in four-dimensional N = 8 supergravity.The second part of the thesis concerns the gaugings of extended supergravities in four dimensions. We first show that the embedding tensor formalism does not allow for deformations that cannot be reached by working with the usual Lagrangian in the duality frame picked by the embedding tensor. We then examine through BRST methods the deformations of a large class of non-minimally coupled scalars and abelian vector fields in four dimensions, of which ungauged supergravities offer a prime example. We prove that all local deformations of these models which modify the gauge transformations are of the usual Yang-Mills type, i.e. correspond to the gauging of some rigid symmetries of the undeformed theory. Combined with the first result, this shows that the embedding tensor formalism correctly captures the most general local deformations of these theories.In the third part, we construct self-contained action principles for several types of free fields in six dimensions, whose field strengths satisfy a self-duality condition. These fields are motivated by two considerations. First, their existence allows for a remarkable geometric interpretation of the electric-magnetic duality symmetries of vector fields and linearized gravity in four dimensions. Second, they appear in the spectrum of the chiral N = (4,0) and N = (3,1) ``exotic supergravities" in place of the usual metric. The free action and supersymmetry transformations for those theories are explicitly constructed. We also check that they reduce to linearized maximal supergravity in five dimensions, thus completing the picture of higher-dimensional parents of N = 8 supergravity, at least at the free level. Along the way, we also generalize previous works on linearized supergravity by other authors, in which the graviton and its dual appear on the same footing at the level of the action.We conclude with some open questions, perspectives for future work, and a series of technical appendices. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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Includes bibliographical references. / The tendency in theoretical physics, particularly in the past few decades, has been towards unification: over the years it has emerged that increasingly many physical phenomena can be explained by a common underlying theory. Symmetry principles, both global and local, play an important role in this unification programme. Global symmetries often account for approximate regularities we observe in nature - local or gauge symmetries are understood as basic symmetries which lie at the heart of the interactions of the constituents of matter.

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This report aims to give an insight to the path integral formalism in quantum mechanics. After explaining the kernel's construction, some of its properties and ways to compute it, we see how it relates to the Schrödinger picture. Moreover, we see how its representation can change if it is defined in the space, momentum, time or energy space. Finally, we derive Born's expansion with the kernel showing how this formalism helps to understand perturbation theory and thus scattering. The path integral formalism is then used in quantum field theory with proofs and examples of simple correlation functions. Furthermore, supersymmetry in zero and one dimension are studied with use of the localization principle and the Witten index.

This thesis presents a search for the supersymmetric partner of the top quark in the final state with one lepton. The search focuses especially in the region of the parameter space where the 2-body decay dominates. The analysis is performed using LHC full Run 2 data at √s = 13 TeV as recorded by the ATLAS detector. No significant excess above the backgrounds is observed, and 95% confidence level exclusion limits are calculated in the stop-neutralino mass plane. Stops are excluded up to 1200 GeV in the low neutralino mass scenario of below 400 GeV. The Tile Calorimeter is part of the ATLAS calorimeter system whose main task is to measure the energy of hadrons. A performance study is conducted on the Tile Calorimeter using muons from W boson decay originating from proton-proton collisions. Each calorimeter cell response is measure in data and compared with detector simulation.  The azimuthal cell response uniformity is also investigated using a likelihood method. Overall, a good data to detector simulation agreement and azimuthal uniformity is observed which shows well-calibrated cells and uniform responses among the calorimeter modules.

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