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2009

Dyson instability for 2D nonlinear O(N) sigma models

Meurice, Y.

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For lattice models with compact field integration (nonlinear sigma models over compact manifolds and gauge theories with compact groups) and satisfying some discrete symmetry, the change of sign of the bare coupling g_0^2 at zero results in a mere discontinuity in the average energy rather than the catastrophic instability occurring in theories with integration over arbitrarily large fields.

This indicates that the large order of perturbative series and the non-perturbative contributions should have unexpected features.
Using the large-N limit of 2-dimensional nonlinear O(N) sigma model, we discuss the complex singularities of the average energy for complex 't Hooft coupling lambda= g_0^2N.
A striking difference with the usual situation is the absence of cut along the negative real axis.

Dyson instability for 2D nonlinear O(N) sigma models · Around

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