THE CUTOFF λϕ4 O(N) MODEL IN THE LARGE N LIMIT

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Abstract
A cutoff version of the λϕ4 O(N) model is considered to leading order in 1/N with particular attention paid to the effective potential, which is surprisingly rich in structure. With suitable restriction on a background classical field, one finds a phenomenologically viable model with spontaneously broken symmetry, a potential bounded below, and amplitudes free of tachyons. The model has an O(N − 1) singlet resonance in both weak and strong couplings, which can be interpreted as the Higgs meson in applications. Further, an unphysical resonance, which can be used to define a triviality scale for the model, appears at a mass above the cutoff mass Λ. The phenomenological aspects of our discussion are consistent with previous studies, whose results are obtained by somewhat different methods. The question of the double-scaling limit for the cutoff model is considered as an application of the effective potential. It is shown that the double-scaling limit is not possible.

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