Some new results on an old controversy: is perturbation theory the correct asymptotic expansion in nonabelian models?

Details Some new results on an old controversy: is perturbation theory the correct asymptotic expansion in nonabelian models? Some new results on an old controversy: is perturbation theory the correct asymptotic expansion in nonabelian models?

2004-06-30

arxiv.org/abs/hep-lat/0406041v2

Phys.Rev. D70 (2004) 107706

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, 3 figures

Scientific paper

10.1103/PhysRevD.70.107706

Several years ago it was found that perturbation theory for two-dimensional O(N) models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided $N>2$. There ensued a discussion whether the boundary conditions introduced to show this phenomenon were somehow anomalous and there was a class of `reasonable' boundary conditions not suffering from this ambiguity. Here we present the results of some computations that may be interpreted as giving some support for the correctness of perturbation theory with conventional boundary conditions; however the fundamental underlying question of the correctness of perturbation theory in these models and in particular the perturbative $\beta$ function remain challenging problems of mathematical physics.

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