Infinite Family of Integrable Sigma Models Using Auxiliary Fields

We introduce a class of 2D sigma models which are parametrized by a function of one variable. In addition to the physical field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>g</a:mi></a:math>, these models include an auxiliary field <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>v</c:mi></c:mrow><c:mrow><c:mi>α</c:mi></c:mrow></c:msub></c:mrow></c:math> which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor.