Certain integrable classical field theories can be formulated as classical affine Gaudin models, where g is an affine Lie algebra. Such classical field theories include the principal chiral model, coset sigma models and affine Toda field theory. As such, affine Gaudin models can be seen as a 'master theory' for integrable systems, but is most naturally formulated in the Hamiltonian formalism, unlike other master theories like four-dimensional Chern–Simons theory or anti-self-dual Yang–Mills.