Hidden Symmetries of the Principal Chiral Model Unveiled

Chand Devchand and Jeremy Schiff

Communications in Mathematical Physics 190 675-695 (1998).

By relating the two-dimensional U(N) Principal Chiral Model to a simple linear system we obtain a free-field parametrisation of solutions. Obvious symmetry transformations on the free-field data give symmetries of the model. In this way all known `hidden symmetries' and Backlund transformations, as well as a host of new symmetries, arise.