ACTION OF HEDGEHOG INSTANTONS IN THE DISORDERED PHASE OF THE (2+1)-DIMENSIONAL CPN-1 MODEL

The large-N limit of the (2 + 1)-dimensional CPN-1 model exhibits hedgehog-like instanton saddle points in its disordered phase. We determine the structure of these saddle points and evaluate the action, Score, of a charge-q instanton. We find that lim ξ a → ∞ limN → ∞ Sscore 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} in the disodered phase. Moreover, the length scale, ξC, with which correlations of U(1) gauge field, Aμ, decay exponentially, is ξC ∼ a( ξ a)N. The length ξC is also the scale at which the matter fields, zα, 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. © 1990.