Related papers: Algebraic Curves for Integrable String Backgrounds

I review the appearance of classical integrable systems as an effective tool for the description of non-perturbative exact results in quantum string and gauge theories. Various aspects of this relation: spectral curves, action-angle…

We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the…

We study the integrable boundaries and crosscaps of classical sigma models. We show that there exists a classical analog of the integrability condition and KT-relation of the boundary and crosscap states of quantum spin chains. We also…

We review basic examples of classical string solutions in AdS5xS5. We concentrate on simplest rigid closed string solutions of circular or folded type described by integrable 1-d Neumann system but mention also various generalizations and…

Several string backgrounds which arise in the AdS/CFT correspondence are described by integrable sigma-models. Their target space is always a Z(4) supercoset (a semi-symmetric superspace). Here we list all semi-symmetric cosets which have…

We elevate $\lambda$-deformed $\sigma$-models into full type-II supergravity backgrounds. We construct several solutions which contain undeformed $AdS_n$ spaces, with $n=2,3,4$ and $6$, as an integrable part. In that respect, our examples…

We systematically study the spectrum of open strings attached to half BPS giant gravitons in the N=4 SYM AdS/CFT setup. We find that some null trajectories along the giant graviton are actually null geodesics of AdS_5x S^5, so that we can…

In this article we discuss gauge/strings correspondence based on the non-critical strings. With this goal we present several remarkable sigma models with the AdS target spaces. The models have kappa symmetry and are completely integrable.…

We introduce a series of articles reviewing various aspects of integrable models relevant to the AdS/CFT correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe…

We perform a first principle semiclassical quantisation of the general finite-gap solution to the equations of a string moving on R x S^3. The derivation is only formal as we do not regularise divergent sums over stability angles. Moreover,…

In this thesis we investigate quantum aspects of the Green-Schwarz superstring in various AdS backgrounds relevant for the AdS/CFT correspondence, providing several examples of perturbative computations in the corresponding integrable…

It is known that classical string dynamics in pure AdS_5\times S^5 is integrable and plays an important role in solvability. This is a deep and central issue in holography. Here we investigate similar classical integrability for a more…

Integrability of the one-dimensional Hubbard model and of the factorised scattering problem encountered on the worldsheet of AdS strings can be expressed in terms of a peculiar quantum algebra. In this article, we derive the classical limit…

We review the recent progress towards applying worldsheet integrability techniques to the $AdS_3/CFT_2$ correspondence to find its all-loop S matrix and Bethe-Yang equations. We study in full detail the massive sector of $AdS_3\times…

This review is devoted to the classical integrability of the AdS5xS5 superstring theory. It starts with a reminder of the corresponding action as a coset model. The symmetries of this action are then reviewed. The classical integrability is…

We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary…

We discuss a formalism for solving (2+1) AdS gravity on Riemann surfaces. In the torus case the equations of motion are solved by two functions f and g, solutions of two independent O(2,1) sigma models, which are distinct because their…

There have been recent advances in the construction of algebraic curves for certain classes of string solutions in the context of the AdS/CFT correspondence. In this paper we obtain the Lax operators and associated spectral curves for…

In these proceedings we review the results of [1-3]. We show on the example of the SU(2) chiral-field how to reproduce the classical finite gap solutions for a large class of integrable sigma models from their exact quantum solutions. These…

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…