Fractionally charged Wilson loops as a probe of θ dependence in CPN-1 sigma models:: Instantons versus large N

The behavior of Wilson loops with fractional charge is used to study the theta dependence of the free energy density epsilon(theta) for the CP1, CP5, and CP9 sigma models in two space-time dimensions. The function epsilon(theta) is extracted from the area law for a Wilson loop of charge q=theta/2 pi. For CP1, epsilon(theta) is smooth in the region theta approximate to pi and well described by a dilute instanton gas throughout the range 0 < 2 pi. For CP5 and CP9 the energy exhibits a clear cusp and evidence for discrete, degenerate vacua at theta=pi, as expected from large N arguments. For CP9 the theta dependence is in good quantitative agreement with the leading-order large N prediction epsilon(theta)=1/2 chi(t)theta(2) throughout the range 0