1203.2256 (Y. Meurice)

Remarks about Dyson's instability in the large-N limit    [PDF]

Y. Meurice

There are known examples of perturbative expansions in the 't Hooft coupling lambdat with a finite radius of convergence. This seems to contradict Dyson's argument stating that the instability at negative coupling implies a zero radius of convergence. Using the example of the linear sigma model in three dimensions, we resolve this paradox. We show that a saddle point persists for negative values of lambdat until it reaches a critical value -|lambdat_c| and that the radius of convergence of the perturbative series is |lambdat_c|. On the other hand, an explicit construction shows that for -|\lambdat_c|< lambdat <0, the effective potential does not exist for large values of the field and not at all if lambdat <-|lambdat_c|. This could be relevant to understand de Sitter instabilities.

View original: http://arxiv.org/abs/1203.2256