Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-03-14
J.Phys.A34:9485-9506,2001
Physics
High Energy Physics
High Energy Physics - Theory
1+32 pages, LaTeX2e, typos corrected
Scientific paper
10.1088/0305-4470/34/44/310
An algebraic criterion for the vanishing of the beta function for renormalizable quantum field theories is presented. Use is made of the descent equations following from the Wess-Zumino consistency condition. In some cases, these equations relate the fully quantized action to a local gauge invariant polynomial. The vanishing of the anomalous dimension of this polynomial enables us to establish a nonrenormalization theorem for the beta function $\beta_g$, stating that if the one-loop order contribution vanishes, then $\beta_g$ will vanish to all orders of perturbation theory. As a by-product, the special case in which $\beta_g$ is only of one-loop order, without further corrections, is also covered. The examples of the N=2,4 supersymmetric Yang-Mills theories are worked out in detail.
Lemes V. E. R.
Sarandy Marcelo S.
Sorella Silvio Paolo
Ventura Ozemar S.
Vilar Luiz C. Q.
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