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The Ads/CFT correspondence of technology.

Abstract : My argument unfolds along two main lines of work. Both arguments are treated a relationship between string theory and phenomenological aspects / cosmological. On the one hand, the noncommutative geometry (NC) is a natural consequence of the presence of branes and fluxes in string theory. The non-commutativity distorts some fundamental properties ordinary theories describing such electro-weak interactions and strong or statistical models. It is in this sense that the geometry represents a CN application to the phenomenology of strings. On the other hand, the branes are the key ingredient in models of brane worlds. The model Randall-Sundrum (RS) in particular, offers new perspectives both from the point of view of cosmology, creating scenarios of cosmological evolution unconventional from the point of view of holography. The first part of the thesis is dedicated to the NC geometry and, in particular, theories NC integrable fields. The main purpose of the work was to study the consequences of non commutativit'e compared al'integrabilite. More precisely, we wanted to verify or refute in a theorem that links the NC, in two dimensions, the integrability is factoring the matrix S. With integrability we speak of the existence of an infinite number of local currents preserved, associated the symmetries of the theory of champs.Le starting point has been to ensure the presence of such currents, using the formalism of the double complex. This method allows to obtain the equations of motion as conditions of int 'egrabilite a linear system of differential equations. has from solutions of linear system even after the current canned. In Weyl operator formalism, the procedure is immediately generalized to the NC geometry. An algebra of functions (Weyl operators) defined on a space is associated with a CN CN algebra or number of functions is executed by an NC Moyal product: the product. By introducing the product in the linear system and deducting the equations of motion CN, we obtain the generalization NC Bicomplex. It was the first model infers in generalizing the double complex of modeledesine Gordon-(SG) geometry NC. We have deduced (in collaboration with Grisaru, Penati, Tamassia) action corresponding to equations of motion previously established by Grisaru and Penati. The calculation of scattering amplitudes and production has determined the characteristics of the S matrix of the model. Acausal behavior have been identified for diffusion process. In addition, the processes of production have a nonzero amplitude: where the non-validity of the theorem of integrability vs.. factorization for this version of the NC model of SG. Other properties have been put in evidence, as the relation with string theory and bosonization. The second model was proposed SG CN in collaboration with Lechtenfeld, Penati, Popov, Tamassia. The equations of motion have been derived from dimensional reduction of the sigma model in 2 +1 dimensional NC, which in turn is the reduction of the theory of self-dual Yang-Mills in 2 +2 dimensions CN (N = describing superstrings 2avecchamps B). The action was calculated that the amplitudes of the same. Production processes possessing zero amplitudes and diffusion ones do not dependent parameter of NC, and lead to causal behavior. The second model seems to obey SG CN has the equivalent between integrability and factorization matrix S. The reduction of string theory retains its validity even at the level of action contrary to the previous model. The second part of my thesis deals with models of brane universes, or more precisely of SAR models. The model proposed by Randall and Sundrumse located in a bulk 5-dimensional, characterized per a symmetry of Z2 orbifold wrt the position of the 4-dimensional brane. Thanks to the warp factor that multiplies the subspace 4-dimensional parallel to the brane, we obtain the location of the modes of the graviton. Therefore, the Newtonian gravitational potential is effective to energies are smaller than Planck mass. By introducing a further term in the bulk material and considering the exchange of energy between brane and bulk, a variety of new cosmologies in drift. In the first part of my work on RS we have proposed a similar model is in a 7-dimensional bulk. The 6-dimensional brane - compactification with two dimensions - is placed at the orbifold fixed point Z2. To study the cosmological evolution when we are in relationship with the observations, we have introduced the exchange of energy between brane and bulk. The possible scenarios are many and depend on the explicit form of the parameter of exchange of energy. Among other things, the fixed points possess a positive acceleration, which may well represent the recent acceleration of the universe. There are also stable for a wide range of parameters values. Finally we can draw scenarios that start from an initial accelerated, passing a succession era of deceleration, to end on a stable fixed point of inflation. The models of universe brane has the RS possess a dual via holographic AdS / CFT. The AdS / CFT establishes a theory of supergravity (or plusg 'en' eral, strings) in a background field of anti de Sitter (AdS) in d + 1 dimensions is dual to a theory of field line (CFT) in d dimensions. Taking into account the differences presented in the two descriptions, this correspondence has been made more precise in the formulation of the holographic renormalization. If space in AdS is regularized by an IR Cutoff, the corresponding CFT RESULT regularized by an ultraviolet cutoff and coupled to the gravity d-dimensional. In analogy al'analyse effected in five dimensions by Kiritsis, we constructed the dual theory to cosmological model SAR in seven dimensions. To capture the dynamics dictated by the exchange of energy between brane and bulk, the six-dimensional holographic theory was generalized to the interacting case (between material and CFT) and non-compliant. The result is the relationship between the mass parameters belonging to two descriptions and the exchange of energy between, on one side, and the interaction parameter, on the other. In addition, the parameter of failure to comply is associated with self-interaction parameter of bulk in the description of seven-dimensional supergravity. The research therefore includes results which may be implemented in the phenomenology and cosmology of the string. On the one hand we investigate the influence of bound al'integrabilite noncommutative model of SG. On the other hand, the cosmological consequences of the location of the RS model in seven dimensions have been studied and the AdS / CFT has been applied to derive information on the theory dual, coupled to gravity.
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Liuba Mazzanti. The Ads/CFT correspondence of technology.. Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]. Ecole Polytechnique X, 2007. English. ⟨pastel-00003164⟩

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