Related papers: Jordanian deformations of the AdS_5xS^5 superstrin…
sl_2 Gaudin model with Jordanian twist is studied. This system can be obtained as the semiclassical limit of the XXX spin chain deformed by the Jordanian twist. The appropriate creation operators that yield the Bethe states of the Gaudin…
The construction elements of the factorised form of the Yang-Baxter R operator acting on generic representations of q-deformed sl(n+1) are studied. We rely on the iterative construction of such representations by the restricted class of…
The quadratic action for physical fields of type IIB supergravity model on $AdS_5\times S^5$ is derived starting from the recently found covariant action. All boundary terms that have to be added to the action to be used in the AdS/CFT…
We discuss the $\beta$-deformation of $AdS_5\times S^5$ which incorporates the $SL(2,\mathbb{R})$ symmetry of the type IIB theory. The axion-dilaton is identified with a two-torus from an eleven dimensional viewpoint. We consider the null…
It is shown that a class of rotating strings in AdS_5 x S^5 with SO(6) angular momenta (J,J',J') preserve 1/8-supersymmetry for large J,J', in which limit they are effectively tensionless; when J=0, supersymmetry is enhanced to 1/4. These…
Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that the spectrum of their deformations can be investigated using…
A two-parametric generalization of the Jordanian deformation $U_h (sl(2))$ of $sl(2)$ is presented. This involves Jacobian elliptic functions. In our deformation $U_{(h,k)}(sl(2))$, for $k^2=1$ one gets back $U_h(sl(2))$. The constuction is…
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 study a local description of composite five-branes of codimension two. The formulation is constructed by virtue of $SL(2,{\mathbb Z}) \times SL(2,{\mathbb Z)}$ monodromy associated with two-torus. Applying conjugate monodromy…
We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r,s) for certain values of (r,s).…
We calculate the first supersymmetric and kappa-symmetric derivative deformation of the M5-brane worldvolume theory in a flat eleven-dimensional background. By applying cohomological techniques we obtain a deformation of the standard…
In this thesis we discuss how one can derive the quantum spectral curve for the $\eta$-deformed AdS$_5 \times S^5$ superstring, an integrable deformation of the AdS$_5 \times $S$^5$ superstring with quantum group symmetry. This model can be…
We derive the Green-Schwarz action on AdS_5 x S^5 using an alternate version of the coset superspace construction. By Wick rotations and Lie algebra identifications we bring the coset to GL(4|4)/(Sp(4) x GL(1))^2, which allows us to…
We consider a generalization of the leading-order matching of coherent state actions for semiclassical states on the super Yang-Mills and the superstring sides of the AdS/CFT duality to sectors with fermions. In particular, we discuss the…
We study the relation between vertex operators in AdS_5 x S^5 and classical spinning string solutions. In the limit of large quantum numbers the treatment of vertex operators becomes semiclassical. In this regime, a given vertex operator…
The eta-deformation of the AdS_5 x S^5 superstring depends on a non-split r matrix for the superalgebra psu(2,2|4). Much of the investigation into this model has considered one particular choice, however there are a number of inequivalent…
The kappa-invariant and supersymmetric actions of D1 and D5-branes in AdS_3 x S^3 are investigated, as well as the action of a D5-brane in an AdS_5 x S^5 background. The action of a D5-brane lying totally in an AdS_3 x S^3 background is…
A systematic approach to the study of semiclassical fluctuations of strings in AdS_5 x S^5 based on the Green-Schwarz formalism is developed. We show that the string partition function is well defined and finite. Issues related to different…
We prove a criterion of when a coaction of a compact Lie group on an algebra of continuous functions on a compact manifold extends to a coaction of deformation quantizations of the Lie group and the algebra. We compute an explicit example…
We consider integrability properties of the superstring on $AdS_{5}\times S^{5}$ background and construct a new one parameter family of currents which satisfies the vanishing curvature condition. We present the Hamiltonian analysis for the…