F. Delduc

An integrable deformation of the AdS_5 x S^5 superstring action

An integrable deformation of the type IIB AdS5×S5 superstring action is presented. The deformed field equations, Lax connection, and κ-symmetry transformations are given. The original psu(2,2|4) symmetry is expected to become q deformed.

On classical q-deformations of integrable σ-models

A bstractA procedure is developed for constructing deformations of integrable σ-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter σ-model introduced a few years ago by C. Klimčík. In the case of the symmetric space σ-model on F/G we obtain a new one-parameter family of integrable σ-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset σ-model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2)/U(1) coset σ-model which interpolates all the way to the SU(1, 1)/U(1) coset σ-model.

Derivation of the action and symmetries of the q-deformed AdS5 × S5 superstring

A bstractWe recently proposed an integrable q-deformation of the AdS5 × S5 superstring action. Here we give details on the hamiltonian origin and construction of this deformation. The procedure is a generalization of the one previously developed for deforming principal chiral and symmetric space σ-models. We also show that the original psu2,2|4

Classical and quantum structure of the compact kählerian sigma models

\mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right)

N=4 mechanics of general (4,4,0) multiplets

symmetry is replaced in the deformed theory by a classical analog of the quantum group Uqpsu2,2|4

Integrable double deformation of the principal chiral model

{U}_q\left(\mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right)\right)