Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-02-13
Nucl.Phys. B512 (1998) 237-249
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 18 pages plus 3 figures using epsf. Substantially revised to correct a factor of 2 error in the previous version of equ
Scientific paper
10.1016/S0550-3213(97)00688-3
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 $\lambda$, 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 $0 < \lambda /g^2 < {4/3} (\frac{N_f}{N} - 1)$, 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.
Olmsted David L.
Schnitzer Howard J.
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