From the mass gap in O(N) to the non-Borel-summability in O(3) and O(4) sigma-models

Abstract

We give an analytical derivation of the mass gap of the O(N) sigma models and investigate a large-order behavior of the weak coupling asymptotic expansion for the energy. For sufficiently large N the series is sign-oscillating, which is expected from the large N solution of the sigma model. However, for N=3 and N=4 the series are sign positive.

4 pages; v2: +1 figure, typos corrected, formula (23) corrected; improved explanation and discussion throughout the text; references added

References in corpus (2)

• Comments on operators with large spin
• Scaling function in AdS/CFT from the O(6) sigma model

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