Concerning the Double Scaling Limit in the $O(N)$ Vector Model in Four-Dimensions

Details Concerning the Double Scaling Limit in the $O(N)$ Vector Model in Four-Dimensions Concerning the Double Scaling Limit in the $O(N)$ Vector Model in Four-Dimensions

1992-06-10

arxiv.org/abs/hep-th/9206045v1

Mod. Phys. Lett. A7 (1992) 2449-2452

Physics

High Energy Physics

High Energy Physics - Theory

6, BRX-TH-333

Scientific paper

The 1/N expansion for the O(N) vector model in four dimensions is reconsidered. It is emphasized that the effective potential for this model becomes everywhere complex just at the critical point, which signals an unstable vacuum. Thus a critical O(N) vector model cannot be consistently defined in the 1/N expansion for four-dimensions, which makes the existence of a double-scaling limit for this theory doubtful.

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