Related papers: Target space supergeometry of $\eta$ and $\lambda$…

Integrable string sigma models on AdS$_3$ backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since…

We derive the part of the Lagrangian for the sigma model on the eta-deformed AdS_5 x S^5 space which is quadratic in fermions and has the full dependence on bosons. We then show that there exists a field redefinition which brings the…

In this PhD thesis we review some aspects of integrable models related to string backgrounds or their deformations. In the first part we develop methods to obtain exact results in the AdS3/CFT2 correspondence. We consider the AdS_3 x S^3 x…

We discuss a quantum deformation of the Green-Schwarz superstring on flat space, arising as a contraction limit of the corresponding deformation of AdS_5 x S^5. This contraction limit turns out to be equivalent to a previously studied limit…

Yang-Baxter string sigma-models provide a systematic way to deform coset geometries, such as $AdS_p \times S^p$, while retaining the $\sigma$-model integrability. It has been shown that the Yang-Baxter deformation in target space is simply…

We consider two integrable deformations of 2d sigma models on supercosets associated with AdS_n x S^n. The first, the "eta-deformation" (based on the Yang-Baxter sigma model), is a one-parameter generalization of the standard superstring…

Two distinct $\eta$-deformations of strings on AdS$_5\times$S$^5$ can be defined; both amount to integrable quantum deformations of the string non-linear sigma model, but only one is itself a superstring background. In this paper we compare…

This thesis is mainly devoted to studying integrable deformations of the ${\rm AdS}_5 \times {\rm S}^5$ superstring and generalized supergravity. We start to give a brief review of the ${\rm AdS}_5 \times {\rm S}^5$ superstring formulated…

Starting with the F/G supercoset model corresponding to the AdS_n x S^n superstring one can define the lambda-model of arXiv:1409.1538 either as a deformation of the F/F gauged WZW model or as an integrable one-parameter generalization of…

Yang-Baxter (YB) deformations of string sigma model provide deformed target spaces. We propose that homogeneous YB deformations always lead to a certain class of $\beta$-twisted backgrounds and represent the bosonic part of the supergravity…

For supercosets with isometry group of the form $\hat{G} \times \hat{G}$, the eta-deformation can be generalised to a two-parameter integrable deformation with independent $q$-deformations of the two copies. We study its kappa-symmetry and…

A general class of deformations of integrable sigma-models with symmetric space F/G target-spaces are found. These deformations involve defining the non-abelian T dual of the sigma-model and then replacing the coupling of the Lagrange…

The S-matrix on the world-sheet theory of the string in AdS5 x S5 has previously been shown to admit a deformation where the symmetry algebra is replaced by the associated quantum group. The case where q is real has been identified as a…

We construct supergravity backgrounds for the integrable eta-deformations of the AdS2 x S2 x T6 and AdS5 x S5 superstring sigma models. The eta-deformation is governed by an R-matrix that solves the non-split modified classical Yang-Baxter…

We determine the constraints imposed on the 10d target superspace geometry by the requirement of classical kappa-symmetry of the Green-Schwarz superstring. In the type I case we find that the background must satisfy a generalization of type…

We consider the ABF background underlying the eta-deformed AdS5 x S5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does…

We study the deformed AdS_5 x S^5 supercoset model of arXiv:1309.5850 which depends on one parameter kappa and has classical quantum group symmetry. We confirm the conjecture that in the "maximal" deformation limit kappa -> infinity this…

Interesting deformations of AdS_5 x S^5 such as the gravity dual of noncommutative SYM and Sch\"odinger spacetimes have recently been shown to be integrable. We clarify questions regarding the reality and integrability properties of the…

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…

The lambda deformation of the pure spinor formalism of the superstring in the $AdS_{5}\times S^{5}$ background is introduced. It is shown that the deformation preserves the integrability as well as the one-loop conformal invariance of its…