Action of hedgehog instantons in the disordered phase of the (2 + 1)-dimensional CP^N-1 model

The large-N limit of the (2 + 1)-dimensional CP^N-1 model exhibits hedgehog-like instanton saddle points in its disordered phase. We determine the structure of these saddle points and evaluate the action, S_core, of a charge-q instanton. We find that lim _{ξ a → ∞} lim_{N → ∞} S_score N = 2ρ{variant}_qln( ξ a), where the order of limits is significant. Here a is the lattice spacing, ξ is the spin correlations length, and ρ{variant}_q are a set of universal constants: ρ{variant}₁ = 0.062296..., ρ{variant}₂ = 0.155548.... Free charge-q instantons therefore occur with a density ∼ a ^-3( ξ a)^{-2Nρ{variant}_q} in the disodered phase. Moreover, the length scale, ξ_C, with which correlations of U(1) gauge field, A_μ, decay exponentially, is ξ_C ∼ a( ξ a)^{N_ρ{variant}1}. The length ξ_C is also the scale at which the matter fields, z^α, experience a confining linear potential. Consequences for spin-Peierls ordering in two-dimensional quantum SU(N) antiferromagnets will be discussed elsewhere, and are briefly noted for completeness.