Lax pairs for new [formula omitted]-symmetric coset σ-models and their Yang-Baxter deformations

Abstract

Two-dimensional σ-models with ZN-symmetric homogeneous target spaces have been shown to be classically integrable when introducing WZ-terms in a particular way. This article continues the search for new models of this type now allowing some kinetic terms to be absent – analogously to the Green-Schwarz superstring σ-model on Z4-symmetric homogeneous spaces. A list of such integrable ZN-symmetric (super)coset σ-models for N≤6 and their Lax pairs is presented. For arbitrary N a big class of integrable models is constructed that includes both the known pure spinor and Green-Schwarz superstring on Z4-symmetric cosets.Integrable Yang-Baxter deformations of this class of ZN-symmetric (super)coset σ-models can be constructed in same way as in the known Z2- or Z4-cases. Deformations based on solutions of the modified classical Yang-Baxter equation, the so-called η-deformation, require deformation of the constants defining the Lagrangian and the corresponding Lax pair. Homogeneous Yang-Baxter deformations (i.e. those based on solutions to the classical Yang-Baxter equation) leave the equations of motion and consequently the Lax pair invariant and are expected to be classically equivalent to the undeformed model.As an example, the relationship between Z3-symmetric homogeneous spaces and nearly (para-)Kähler geometries is revisited. Confirming existing literature it is shown that the integrable choice of WZ-term in the Z3-symmetric coset σ-model associated to a nearly Kähler background gives an imaginary contribution to the action.