C P 2 S Sigma Models Described Through Hypergeometric Orthogonal Polynomials

The main objective of this paper is to establish a new connection between the Hermitian rank-1 projector solutions of the Euclidean CP2S sigma model in two dimensions and the particular hypergeometric orthogonal polynomials called Krawtchouk polynomials. We show that any Veronese subsequent analytical solutions of the CP2S model, defined on the Riemann sphere and having a finite action, can be explicitly parametrized in terms of these polynomials. We apply these results to the analysis of surfaces associated with CP2S models defined using the generalized Weierstrass formula for immersion. We show that these surfaces are homeomorphic to spheres in the su(2s+1) algebra and express several other geometrical characteristics in terms of the Krawtchouk polynomials. Finally, a connection between the su(2) spin-s representation and the CP2S model is explored in detail.