Integrable Coupled σ Models

Abstract

A systematic procedure for constructing classical integrable field theories with arbitrarily many free parameters is outlined. It is based on the recent interpretation of integrable field theories as realisations of affine Gaudin models. In this language, one can associate integrable field theories with affine Gaudin models having arbitrarily many sites. We present the result of applying this general procedure to couple together an arbitrary number of principal chiral model fields on the same Lie group, each with a Wess-Zumino term.

Gauge Theory And Integrability, II

“…It turns out that the model obtained this way coincides precisely with the coupled sigma model introduced recently in connection with the affine Gaudin model [41,42].…”

“…. (12.23) In the language of [41,42] these are the twist functions for an affine Gaudin model; in our context these functions specify the one-form ω.…”

Strong integrability of λ-deformed models

“…k i k j ∂B d 2 σ Tr J i+ λ −1 −1 ij J j− + · · · , (4.1) 9 Under the redefinitions (η,η, K) → (2η, 2ζ, 1 8t ) and for c 2 = −1 (complex branch). 10 A perhaps related class of integrable σ-models was recently constructed in [38,19], based on [39], following a Hamiltonian approach. The precise relation to the models of [37] remains to be elucidated.…”

Field theory and λ-deformations: Expanding around the identity

“…Finally, we believe that, as technique, the free field expansion, with appropriate modifications will be useful in determining anomalous dimensions and quantum properties in general of operators in the so-called η-deformations [31][32][33][34][35][36] using their also their relation to λ-deformations [37][38][39]. Similar comment applies for the integrable coupled σ-models of [40,41].…”