Abstract
A multi-parameter integrable deformation of the principal chiral model is presented. The Yang-Baxter and bi-Yang-Baxter σ-models, the principal chiral model plus a Wess-Zumino term and the TsT transformation of the principal chiral model are all recovered when the appropriate deformation parameters vanish. When the Lie group is SU(2), we show that this four-parameter integrable deformation of the SU(2) principal chiral model corresponds to the Lukyanov model.
Highlights
The Yang-Baxter σ-model can be generalised to a two-parameter integrable deformation of the PCM, the bi-Yang-Baxter σ-model [8, 9], which incorporates the oneparameter Yang-Baxter deformation of the symmetric space σ-model [10] for cosets of the type (G × G)/Gdiag
In this paper we present a multi-parameter deformation of the PCM for a general group G that incorporates each of the models introduced above
In this paper we have presented a new multi-parameter integrable deformation of the PCM for a general group G
Summary
We construct a three-parameter integrable deformation of the PCM Two of these parameters correspond to those of the bi-Yang-Baxter σ-model while the third is the coupling to the WZ term. To obtain this integrable deformation of the PCM we employ on the following strategy. To determine a Lax pair, we will have to explicitly invert operators such as Oab. Without introducing a gauge field, the Gdiag gauge invariance would be ensured by making use of the projector onto the orthogonal complement of the diagonal subalgebra of g ⊕ g Without introducing a gauge field, the Gdiag gauge invariance would be ensured by making use of the projector onto the orthogonal complement of the diagonal subalgebra of g ⊕ g
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