Abstract
Two-dimensional CP n−1 models are considered within the 1 n expansion. Space-time is taken to be a sphere, which provides an infrared cut-off. In a sector with fixed topological charge the leading term of the 1 n expansion of the partition function is calculated exactly and its volume dependence is studied. In the limit of small volume it approaches the semiclassical instanton contribution. For large volumes it represents a flat gaussian distribution of topological charge number. The large- n and large volume limits do not commute.
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