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arXiv · hep-th/9602069

The Gauged Vector Model in Four-Dimensions: Resolution of an Old Problem?

David L. Olmsted·Howard J. Schnitzer
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Abstract

A calculation of the renormalization group improved effective potential for the gauged U(N) vector model, coupled to $N_f$ fermions in the fundamental representation, computed to leading order in 1/N, all orders in the scalar self-coupling $λ$, and lowest order in gauge coupling $g^2$, with $N_f$ of order $N$, is presented. It is shown that the theory has two phases, one of which is asymptotically free, and the other not, where the asymptotically free phase occurs if $0 < λ/g^2 < {4/3} (\frac{N_f}{N} - 1)$, and $\frac{N_f}{N} < {11/2}$. In the asymptotically free phase, the effective potential behaves qualitatively like the tree-level potential. In the other phase, the theory exhibits all the difficulties of the ungauged $(g^2 = 0)$ vector model. Therefore the theory appears to be consistent (only) in the asymptotically free phase.

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David L. Olmsted, Howard J. Schnitzer. 1997-07-15. The Gauged Vector Model in Four-Dimensions: Resolution of an Old Problem?. https://doi.org/10.1016/s0550-3213(97)00688-3

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