On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
Abstract
One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in two-dimensional sigma-models and in the AdS/CFT context. The first part is focused on the AdS5/CFT4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS5 x S5 are discussed in both pure spinor and Green-Schwarz formulations. The second part is dedicated to the AdS4/CFT3 duality with particular attention to the type IIA superstring on AdS4 x CP3 and its integrability. This review is based on a shortened and revised version of the author's PhD thesis, discussed at Uppsala University in September 2009.
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