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

Abstract

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.

6, BRX-TH-333

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• PT-symmetric interpretation of double-scaling
• The Gauged Vector Model in Four-Dimensions: Resolution of an Old Problem?
• Double-Scaling Limit of the O(N)-Symmetric Anharmonic Oscillator