Point particle E-models

Abstract

We show that the same algebraic data that permit to construct the Lax pair and the $r$-matrix of an integrable non-linear $\sigma$-model in $1+1$ dimensions can be also used for the construction of Lax pairs and of $r$-matrices of several other non-trivial integrable theories in $1+0$ dimension. We call those new integrable theories the point particle $\mathcal{E}$-models, we describe their structure and give their physical interpretation. We work out in detail the point particle $\mathcal{E}$-models associated to the bi-Yang-Baxter deformation of the $SU(N)$ principal chiral model. In particular, for each complex flag manifold we thus obtain a two-parameter family of integrable models living on it.

32 pages, references added

References in corpus (4)

• 4-dimensional Chern-Simons theory and integrable field theories
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Integrable $\mathcal{E}$-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
• RG flow of integrable $\mathcal{E}$-models