Heterotic integrable deformation of the principal chiral model

A novel classically integrable model is proposed. It is a deformation of the two-dimensional principal chiral model, embedded into a heterotic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>σ</a:mi></a:math> model by a particular heterotic gauge field. This is inspired by the bosonic part of the heterotic <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>σ</c:mi></c:math> model and its recent Hamiltonian formulation in terms of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi mathvariant="normal">O</e:mi><e:mo stretchy="false">(</e:mo><e:mi>d</e:mi><e:mo>,</e:mo><e:mi>d</e:mi><e:mo>+</e:mo><e:mi>n</e:mi><e:mo stretchy="false">)</e:mo></e:mrow></e:math>-generalized geometry in Hatsuda [Gauged double field theory, current algebras and heterotic sigma models, ]. Classical integrability is shown by the construction of a Lax pair and a classical <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi mathvariant="script">R</j:mi></j:math> matrix. The latter is almost of the canonical form with a twist function and solves the classical Yang-Baxter equation.