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A multi-parameter integrable deformation of the principal chiral model ispresented. The Yang-Baxter and bi-Yang-Baxter sigma-models, the principalchiral model plus a Wess-Zumino term and the TsT transformation of theprincipal chiral model are all recovered when the appropriate deformationparameters vanish. When the Lie group is SU(2), we show that thisfour-parameter integrable deformation of the SU(2) principal chiral modelcorresponds to the Lukyanov model.

Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model