Related papers: Jordanian deformations of the AdS_5xS^5 superstrin…
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 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…
We explore integrability properties of superstring equations of motion in AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges and construct a Lax representation for the corresponding Hamiltonian dynamics on…
We review some recent developments in the construction of integrable $\eta$- and $\lambda$-deformations of the $AdS_5 \times S^5$ superstring. We highlight their link with Poisson-Lie T-duality.
The purpose of this contribution is to initiate the study of integrable deformations for different superstring theory formalisms that manifest the property of (classical) integrability. In this paper we choose the hybrid formalism of the…
We explicitly derive Lax pairs for string theories on Yang-Baxter deformed backgrounds, 1) gravity duals for noncommutative gauge theories, 2) $\gamma$-deformations of S$^5$, 3) Schr\"odinger spacetimes and 4) abelian twists of the global…
We discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. T-duality along four directions in Poincare parametrization of AdS5 maps the bosonic part of the superstring action…
We study the properties of the vertex operator for the beta-deformation of the superstring in AdS(5) x S(5) in the pure spinor formalism. We discuss the action of supersymmetry on the infinitesimal beta-deformation, the application of the…
We derive the gravity duals of noncommutative gauge theories from the Yang-Baxter sigma model description of the AdS_5xS^5 superstring with classical r-matrices. The corresponding classical r-matrices are 1) solutions of the classical…
We construct an Anti-de Sitter(AdS) algebra in a nondegenerate superspace. Based on this algebra we construct a covariant kappa-symmetric superstring action, and we examine its dynamics: Although this action reduces to the usual…
Two type of superization of the Jordanian r-matrix for the Lie algebra sl(2) are considered. One type is associated with the Lie superalgebra sl(1|1) and another type is associated with the orthosymplectic Lie superalgebra osp(1|2).…
We proceed to study the integrable structures of two-dimensional non-linear sigma models defined on three-dimensional Schrodinger spacetimes. We show that anisotropic Lax pairs are equivalent with isotropic Lax pairs with flat conserved…
It is shown that a supersymmetric and $\kappa$-symmetric D3-brane action on $AdS_5 \times S^5$ is mapped into itself by a duality transformaion, thereby verifying the $SL(2,Z)$ invariance of the D3-brane action in the $AdS_5 \times S^5$…
As part of program to quantize superstrings in AdS_5 x S^5 background in light cone approach we find the explicit form of the corresponding Green-Schwarz action in fermionic light-cone kappa-symmetry gauge. The resulting action is quadratic…
We present the construction of the $\lambda$-deformation of $AdS_5\times S^5$ superstring from the four dimensional Chern-Simons-type gauge theory. The procedure is applicable to all the semi-symmetric coset models and generalizes the…
The contraction and Jordan-Schwinger construction connect the $su(2)$ and the heisenberg algebra, going in oposite directions. This persists in the q-deformed cases, but in a slightly different way. This work investigates this further,…
Recently Lunin and Maldacena used an SL(3,R) transformation of the AdS_5 x S^5 background to generate a supergravity solution dual to a so-called beta-deformation of N = 4 super Yang-Mills theory. We use a T-duality-shift-T-duality (TsT)…
We compute some normalized structure constants in the $\eta$-deformed $AdS_5\times S^5$ in the framework of the semiclassical approach. This is done for the cases when the "heavy" string states are finite-size giant magnons carrying one…
This paper suveys some recent algebraic developments in two parameter Quantum deformations and their Nonstandard (or Jordanian) counterparts. In particular, we discuss the contraction procedure and the quantum group homomorphisms associated…
Homogeneous Yang-Baxter (YB) deformation of AdS$_5\times$S$^5$ superstring is revisited. We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB deformations are equivalent to…