Abstract
The behavior of Wilson loops with fractional charge is used to study the {theta} dependence of the free energy density {epsilon}({theta}) for the CP{sup 1}, CP{sup 5}, and CP{sup 9} 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 CP{sup 1}, {epsilon}({theta}) is smooth in the region {theta}{approx_equal}{pi} and well described by a dilute instanton gas throughout the range 0<{theta}<2{pi}. For CP{sup 5} and CP{sup 9} the energy exhibits a clear cusp and evidence for discrete, degenerate vacua at {theta}={pi}, as expected from large N arguments. For CP{sup 9} the {theta} dependence is in good quantitative agreement with the leading-order large N prediction {epsilon}({theta})=(1/2){chi}{sub t}{theta}{sup 2} throughout the range 0<{theta}<{pi}.
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