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Théorie F en huit dimensions : une perspective de la Théorie des Champs Exceptionnels et de la Théorie des Cordes Hétérotique

Abstract : One of the most promising theories to unify quantum mechanics and general relativity is currently string theory. The search for a supersymmetric formulation of strings led to five consistent ten dimensional superstring theories which were later unified under the scope of M-theory. The fundamental aspect of this unification is the discovery of a web of dualities between the five superstring theories and eleven dimensional supergravity.This thesis addresses dualities in the context of F-theory in eight dimensions. F-theory is twelve dimensional and provides a non-perturbative formulation of type IIB supergravity with 7-branes. On the other hand exceptional field theory provides a U-dual formulation of type IIB supergravity and we therefore focus on the possible links between these two formulations. F-theory is also conjectured to be dual to the heterotic string in 8 dimensions. The gauge group appears radically differently in these two formulations. In F-theory it is interpreted as a particular algebraic structure of an elliptically fibered K3 surface, while on the heterotic string it is principally determined the Wilson lines. Although studied in the context of type IIB string theory, the explicit map between the moduli in F-theory and its heterotic dual are still quite unknown.In the first part of this thesis we present basic notions of string theory, compactifications, branes and dualities. In the second one, we show that R+ X E₃(₃) exceptional field theory in eight dimensions can incorporate aspects of F-theory in a specific setting, and in particular describes the monodromies of (p; q) 7-branes. Finally, in the third part we study the duality between F-theory compactified on an elliptic K3 surface and the heterotic string on a two-torus. We present how to construct elliptically fibered K3 surfaces via reflexive polytopes which can be understood in terms of Wilson lines in the dual heterotic string theory.
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Lilian Chabrol. Théorie F en huit dimensions : une perspective de la Théorie des Champs Exceptionnels et de la Théorie des Cordes Hétérotique. High Energy Physics - Theory [hep-th]. Université Paris-Saclay, 2020. English. ⟨NNT : 2020UPASP018⟩. ⟨tel-03015857⟩

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