Michel Grundland, UQTR et CRM

This talk is devoted to the study of an invariant formulation of completely integrable ${C}P^{N-1}$ Euclidean sigma models in two dimensions, defined on the Riemann sphere, having finite actions. Surfaces connected with the ${C}P^{N-1}$ models, invariant recurrence relations linking the successive projection operators and immersion functions of the surfaces are discussed in detail. Making use of the fact that the immersion functions of the surface satisfy the same Euler-Lagrange equations as the original projector variables, we derive surfaces induced by surfaces and prove that the stacked surfaces coincide with each other, which demonstrates the idempotency of the recurrent procedure. We also show that the ${C}P^{N-1}$ model equations admit larger classes of solutions than the ones corresponding to rank-1 Hermitian projectors.