Abstract
The mass gap for the quantum O( N) non-linear sigma model in a finite volume in two dimensions is calculated to two-loop order in perturbation theory. This result is used to estimate the mass gap of the infinite-volume O(3) model to be about 2.1 Λ MS ± 10% . The calculation is carried out using dimensional regularization with both compact and non-compact extra dimensions, with the same result in both cases.
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