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Abstract In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern–Simons theory, we derive a simple and unifying two-dimensional form for the action of many integrable σ -models which are known to admit descriptions as affine Gaudin models. This includes both the Yang–Baxter deformation and the λ -deformation of the principal chiral model. We also give an interpretation of Poisson–Lie T -duality in this setting and derive the action of the E E -model.
Delduc et al. (Sat,) studied this question.
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