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Derivation of the action and symmetries of the \(q\)-deformed \({\mathrm{AdS}}_5\times S^5\) superstring. (English) Zbl 1333.81322
Summary: We recently proposed an integrable \(q\)-deformation of the \({\mathrm{AdS}}_5\times S^5\) 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 \(\mathfrak{psu}(2,2|4)\) symmetry is replaced in the deformed theory by a classical analog of the quantum group \(U_q(\mathfrak{psu}(2,2|4))\) with \(q\) real. The relation between \(q\) and the deformation parameter \(\eta\) 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 \(\mathrm{dS}_5\times H^5\). Finally, we discuss the various freedoms in the construction.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
81T60 Supersymmetric field theories in quantum mechanics
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