Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring

TL;DR

This paper details the Hamiltonian derivation of a q-deformed AdS_5 x S^5 superstring, revealing how the original symmetry is replaced by a quantum group and exploring the deformation's properties and limits.

Contribution

It provides a Hamiltonian-based construction of the integrable q-deformation of the AdS_5 x S^5 superstring and analyzes its symmetry structure and deformation limits.

Findings

Original symmetry replaced by a classical quantum group U_q(psu(2,2|4))

Deformation relates to a parameter q with explicit relation given

Maximal deformation limit yields an undeformed semi-symmetric space sigma-model

Abstract

We recently proposed an integrable q-deformation of the AdS_5 x 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 sigma-models. We also show that the original psu(2,2|4) symmetry is replaced in the deformed theory by a classical analog of the quantum group U_q(psu(2,2|4)) with q real. The relation between q and the deformation parameter 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 sigma-model with bosonic part dS_5 x H^5. Finally, we discuss the various freedoms in the construction.