Abstract
We define a two-parameter family of integrable deformations of the principal chiral model on an arbitrary compact group. The Yang–Baxter σ-model and the principal chiral model with a Wess–Zumino term both correspond to limits in which one of the two parameters vanishes.
Highlights
Rajeev in [1] that there exists a one-parameter deformation of the Poisson brackets satisfied by the current of the principal chiral model
This agrees with the one-parameter deformation of the Poisson brackets of the principal chiral model
In this note we presented a two-parameter deformation of the principal chiral model
Summary
Rajeev in [1] that there exists a one-parameter deformation of the Poisson brackets satisfied by the current of the principal chiral model. It turns out that the Kac-Moody currents are either both real or complex conjugate of one another, depending on the value of the deformation parameter [2]. We will refer to these two branches in the deformation parameter as real and complex, respectively. The integrable field theory which provides a realisation of the deformed Poisson algebra is known. As was shown in [3], for the complex branch this is the Yang-Baxter σ-model defined by C. In this note we exhibit the action of the integrable field theory which realises the double deformation in the complex branch
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