Integrabilité dans la Correspondance AdS/CFT:
l'analyse quasiclassique et l'approche de bootstrap

Abstract : In this thesis we consider a quasi-classical method applicable to integrable field theories which is based on classical integrable structure - the algebraic curve. We apply it to the Green-Schwarz superstring on AdS5 £ S5 space. We show that the proposed method reproduces perfectly the earlier results obtained by expanding the string action for some simple classical solutions. The construction is explicitly covariant and is not based on a particular parametrization of the fields and as a result is free from ambiguities. On the other hand, the finite size corrections in some particulary important scaling limit are studied in this thesis for a system of Bethe equations. For the general superalgebra su(NjK) the result for the 1/L corrections obtained. We find an integral equation which describes these corrections in a closed form. As a by-product of this computation we found a new type of the duality among the systems of Bethe equations. As an application we consider the conjectured Beisert-Staudacher (BS) equations with the Hernandez-Lopez dressing factor where the finite size corrections should reproduce quasi-classical results around general classical solution. Indeed, we show that our integral equation can be interpreted as a sum of all physical fluctuations and thus prove the complete 1-loop consistency of the BS equations. We demonstrate that any local conserved charge (including the AdS Energy) computed from the BS equations is indeed given at 1-loop by the sum of charges of fluctuations with an exponential precision for large S5 angular momentum of the string. As an independent result, the BS equations in su(2) sub-sector were derived from the Zamolodchikovs' S-matrix.
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Nikolay Gromov. Integrabilité dans la Correspondance AdS/CFT:
l'analyse quasiclassique et l'approche de bootstrap. Mathematical Physics [math-ph]. Université Pierre et Marie Curie - Paris VI, 2007. English. ⟨tel-00286218⟩

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