Toda! Toda! Toda!

(schematic for post)

Here is the Lagrangian. The m and b are parameters under your control and the n's are the coefficients of the maximal root in terms of the other roots.

The reason this is so super special awesome is in its integrability and how it reduces to lots of simpler integrable field theories. Examples include the sine-gordon model when you use a pathetically small r.

Even better it describes integrable deformation of a generalized Lioville theory.

If you analytically continue to imaginary b, sometimes you get deformations of minimal models. Magnetic deformation of an Ising model. Yay! actual physical relevance.