Auxiliary Field Sigma Models and Yang-Baxter Deformations

2024/08/19 by Daniele Bielli, Christian Ferko, Bielli, Daniele +5 · 3 citations
Mathematics · Engineering · #Advanced Topics in Algebra #Intermetallics and Advanced Alloy Properties #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2408.09714

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 \mathfrakg. In the YB case, our construction produces one integrable deformation for each pair (R, E), where R is an antisymmetric bilinear operator on \mathfrakg 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,R, E), where R is another antisymmetric bilinear operator on \mathfrakg and obeys the non-split inhomogeneous 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.

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• Relating auxiliary field formulations of 4d duality-invariant and 2d integrable field theories
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