Auxiliary field sigma models and Yang-Baxter deformations - Daniele Bielli; Christian Ferko; Liam Smith; Gabriele Tartaglino-Mazzucchelli (Journal of High Energy Physics)
Abstract We combine the Yang-Baxter (YB) and bi-Yang-Baxter (bi-YB) deformations with higher-spin auxiliary field deformations to construct multi-parameter families of integrable deformations of the principal chiral model on a Lie group G with semi-simple Lie algebra g $$ \mathfrak{g} $$ . In the YB case, our construction produces one integrable deformation for each pair ( R $$ \mathcal{R} $$ , E), where R $$ \mathcal{R} $$ is an antisymmetric bilinear operator on g $$ \mathfrak{g} $$ obeying the modified classical Yang-Baxter equation and E is a function of several variables. In the bi-YB case, the pair becomes a triplet ( R $$ \mathcal{R} $$ , R ~ $$ \overset{\sim }{\mathcal{R}} $$ , E), where R ~ $$ \overset{\sim }{\mathcal{R}} $$ is another antisymmetric bilinear operator on g $$ \mathfrak{g} $$ obeying the modified classical Yang-Baxter equation. We show that every model in these families is (weakly) classically integrable by exhibiting a Lax representation for their equations of motion.