This book addresses several aspects of the integrable structure of the AdS/CFT correspondence. In particular it presents computations made on both sides of the AdS/CFT correspondence, at weak and at strong coupling. On the string theory side of the correspondence, the book focuses on the evaluation of the energy spectrum of closed string solutions moving in some deformed backgrounds that preserve integrability. On the gauge theory side, it explores various formal problems arising in the computation of two and three-point functions by means of the Algebraic Bethe Ansatz and the Quantum Inverse Scattering method. The book features numerous results on integrability in the context of the AdS/CFT correspondence. Self-contained and pedagogical, it includes general discussions and detailed presentations on the use of integrable systems techniques and their applications.
The author graduated from the Universidad Autónoma de Madrid, where he also received his Master in Theoretical Physics. After that he moved to the Universidad Complutense de Madrid, where he worked on his Ph.D. with Rafael Hernandez. During this time he visited the Institute de Physique Théorique at Saclay (France), where he collaborated with Ivan Kostov and Didina Serban.
Part I: Introduction.- Integrability in the AdS/CFT Correspondence.- Part II: Integrability on the String Theory Side.- Strings in Coset Spaces.- Flux-deformed Neumann-Rosochatius System.- ?
-Deformed Neumann-Rosochatius System.- Part III: Integrability on the Field Theory Side. Spin Chains.- Introduction: The Two Bethe Ansätze.- Two-points Functions and ABA.- Tailoring and Hexagon Form Factors.- Part IV: Conclusions.- Summary and Conclusions.