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We combine the Yang-Baxter deformation with higher-spin auxiliary field deformations to construct a multi-parameter family of integrable deformations of the principal chiral model on a Lie group G with semi-simple Lie algebra g. Our construction produces one integrable deformation for each pair (R, E), where R is an antisymmetric bilinear operator on g obeying the modified classical Yang-Baxter equation and E is a function of several variables. We show that every model in this family is (weakly) classically integrable by exhibiting a Lax representation for its equations of motion.
Bielli et al. (Mon,) studied this question.