Ten-dimensional superstring theory (or the conjectured nonperturbative Mtheory in eleven dimensions) is the most promising candidate for a consistent quantum theory of gravity capable of unifying all known forces of nature. An important question concerning these fundamental theories is how they compactify to lower dimensions and how to obtain a real four dimensional world? In this dissertation we present new avenues for M/string theory to reduce to lower dimensions as well as to four dimensions. For example, we show that by performing a generalized Kaluza-Klein IR reduction on the low-energy field theory of the heterotic string, the resulting lower dimensional theory compactifies spontaneously on S3 to give rise to (Minkowski)6 spacetime. Furthermore, a generalized reduction of M-theory on K3 × IR compacti- fies spontaneously on S2 to give rise to a (Minkowski)4 spacetime. The generalized Kaluza-Klein reduction gauges the Cremmer-Julia type global symmetry and the homogeneous rescaling symmetry of the supergravity equations of motion by giving the higher dimensional fields an additional dependence on the circle coordinate. We apply the generalized reduction scheme to half-maximal supergravities which are obtained from the heterotic string (or the NS-NS sector of the type-II string) compactified on a (10 − D)-dimensional torus truncated to the pure supergravity multiplet. This gives rise to new gauged supergravities in diverse dimensions with supersymmetric Minkowski × sphere vacua.Since two large extra dimensions have received much attention recently, we make a detailed study of the gauged D = 6, N = (1, 1) supergravity. In particular, we show that this theory allows for a consistent sphere reduction on S2 to give rise to D = 4, N = 2 supergravity coupled to a vector multiplet which can further be truncated to N = 1 supergravity with a chiral multiplet. We also investigate pp-waves in AdS backgrounds, i.e. pp-waves as solutions of gauged supergravities with AdS vacua. These solutions generically preserve 1 4 of the supersymmetry. We demonstrate supernumerary supersymmetries for both purely gravitational pp-waves and pp-waves supported by fields strengths. These new backgrounds provide interesting novel features of the supersymmetry enhancement for the dual conformal field theory in the infinite-momentum frame.

A complete non trivial supersymmetric deformation of the maximal supergravity in two dimensions is achieved by the gauging of a SO(9) group. The resulting theory describes the reduction of type IIA supergravity on an AdS_2 x S^8 background and is of first importance in the Domain-Wall / Quantum Field theory correspondence for the D0-brane case. To prepare the construction of the SO(9) gauged maximal supergravity, we focus on the eleven dimensional supergravity and the maximal supergravity in three dimensions since they give rise to important off-shell inequivalent formulations of the ungauged theory in two dimensions. The embedding tensor formalism is presented, allowing for a general desciption of the gaugings consistent with supersymmetry. The SO(9) supergravity is explicitly constructed and applications are considered. In particular, an embedding of the bosonic sector of the two-dimensional theory into type IIA supergravity is obtained. Hence, the Cartan truncation of the SO(9) supergravity is proved to be consistent. This motivated holographic applications. Therefore, correlation functions for operators in dual Matrix models are derived from the study of gravity side excitations around half BPS backgrounds. These results are fully discussed and outlooks are presented.

Nous avons réalisé une déformation non-triviale et complète de la théorie de supergravité maximale en dimension deux. Il s'agit de la supergravité maximale avec groupe de jauge SO(9). Cette théorie décrit de manière effective la supergravité de type IIA sur un espace-temps produit AdS_2 x S^8. Elle joue ainsi un rôle important dans la correspondance Gravité / Théorie de Jauge appliquée au cas de la D0-brane. Afin de préparer la construction de la supergravité maximale jaugée SO(9), nous nous intéressons aux supergravités maximales en dimension onze et trois, puisqu'elles donnent lieu à différentes formulations non équivalentes de la théorie bidimensionnelle non jaugée. Le formalisme d' « Embedding tensor » est ensuite présenté. Il permet de déterminer l'ensemble des groupes de jauges compatibles avec la supersymétrie maximale. La supergravité SO(9) est dès lors explicitement construite et ouvre la voie à deux applications importantes. P our commencer, nous avons réalisé l'inclusion d'un sous-secteur bosonique de la théorie SO(9), la troncature de Cartan, dans la supergravité de type IIA à dix dimensions d'espace-temps. Il s'agit d'une inclusion cohérente. Cela a motivé la deuxième application, de nature holographique. Ainsi, à partir du sous-secteur de Cartan de la supergravité SO(9), et en particulier de la découverte d'états fondamentaux de type « half-BPS », nous avons calculé un ensemble de fonctions de corrélation à un et deux points associées à des opérateurs de modèles de matrice duaux. Nous avons conclu en un résumé de nos travaux et en la présentation d'intéressantes perspectives. / A complete non trivial supersymmetric deformation of the maximal supergravity in two dimensions is achieved by the gauging of a SO(9) group. The resulting theory describes the reduction of type IIA supergravity on an AdS_2 x S^8 background and is of first importance in the Domain-Wall / Quantum Field theory correspondence for the D0-brane case. To prepare the construction of the SO(9) gauged maximal supergravity, we focus on the eleven dimensional supergravity and the maximal supergravity in three dimensions since they give rise to important off-shell inequivalent formulations of the ungauged theory in two dimensions. The embedding tensor formalism is presented, allowing for a general desciption of the gaugings consistent with supersymmetry. The SO(9) supergravity is explicitly constructed and applications are considered. In particular, an embedding of the bosonic sector of the two-dimensional theory into type IIA supergravity is obtained. Hence, the Cartan truncation of the SO(9) supergravity is proved to be consistent. This motivated holographic applications. Therefore, correlation functions for operators in dual Matrix models are derived from the study of gravity side excitations around half BPS backgrounds. These results are fully discussed and outlooks are presented.