A unifying 2D action for integrable $$\sigma $$-models from 4D Chern–Simons theory
F. Delduc, Sylvain Lacroix, M. Magro, Benoît Vicedo
Abstract
Abstract In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern–Simons theory, we derive a simple and unifying two-dimensional form for the action of many integrable $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi></mml:math> -models which are known to admit descriptions as affine Gaudin models. This includes both the Yang–Baxter deformation and the $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>λ</mml:mi></mml:math> -deformation of the principal chiral model. We also give an interpretation of Poisson–Lie T -duality in this setting and derive the action of the $$\textsf {E} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>E</mml:mi></mml:math> -model.