Derivation of the action and symmetries of the q-deformed AdS5 × S 5 superstring

Abstract

We recently proposed an integrable q-deformation of the AdS5 × S 5 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 $$ \mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right) $$ symmetry is replaced in the deformed theory by a classical analog of the quantum group $$ {U}_q\left(\mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right)\right) $$ with q real. The relation between q and the deformation parameter η entering the action is given. The framework used to derive the deformation also enables to prove that at the hamiltonian level, the “maximal deformation” limit corresponds to an undeformed semi-symmetric space σ-model with bosonic part dS5 × H 5. Finally, we discuss the various freedoms in the construction.