Integrable strings for AdS/CFT

Abstract

In this thesis we discuss certain models that arise in string theory, motivated by the AdS/CFT correspondence. For these models there exists a notion of “quantum Integrability”. Although this term is very broad, for us it will be used in the sense of factorisation of scattering for models in 1+1 dimensions. In particular, a process involving N incoming particles will always produce N outgoing particles—particle production and annihilation are not allowed—and the set of momenta will be just reshuffled after scattering. Moreover, an N -> N process will be factorised and rewritten as a sequence of simpler 2 -> 2 processes. The consistency condition for this factorisation is called the Yang-Baxter equation. The background fields that we have derived are NOT compatible with the Bianchi identities and the equations of motion of type IIB supergravity. At this point two scenarios are possible: the first one is that the _-deformed model is just not a type IIB superstring theory; the second one is that there exist further redefinitions of the bosonic and fermionic fields, such that the form of the action as well as the couplings to metric and B-field remain invariant, while the couplings to the Ramond-Ramond fields are modified in such a way that the new answer is compatible with the equations of motion of IIB supergravity. We elaborate on this possibility, and we note that our result reproduces a genuine type IIB background—known as Maldacena-Russo—when a special limit of the deformed action is taken.