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Home > Journal of High Energy Physics (Springer/SISSA) > Derivation of the action and symmetries of the q -deformed AdS 5 × S 5 superstring |

Delduc, F. (Laboratoire de Physique, ENS Lyon et CNRS UMR 5672, Université de Lyon, 46, allée d’Italie, 69364, LYON Cedex 07, France) ; Magro, M. (Laboratoire de Physique, ENS Lyon et CNRS UMR 5672, Université de Lyon, 46, allée d’Italie, 69364, LYON Cedex 07, France) ; Vicedo, B. (School of Physics, Astronomy and Mathematics, University of Hertfordshire, College Lane, Hatfield, AL10 9AB, United Kingdom)

23 October 2014

**Abstract: **We recently proposed an integrable q -deformation of the AdS 5 × 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 p s u 2 , 2 | 4 $$ \mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right) $$ symmetry is replaced in the deformed theory by a classical analog of the quantum group U q p s u 2 , 2 | 4 $$ {U}_q\left(\mathfrak{p}\mathfrak{s}\mathfrak{u}\left(2,2\Big|4\right)\right) $$ 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 dS 5 × H 5 . Finally, we discuss the various freedoms in the construction.

**Published in: ****JHEP 1410 (2014) 132**
**Published by: **Springer/SISSA

**DOI: **10.1007/JHEP10(2014)132

**arXiv: **1406.6286

**License: **CC-BY-4.0