An Algebraic Criterion for the Ultraviolet Finiteness of Quantum Field Theories

Lemes, V. E. R.; Sarandy, M. S.; Sorella, S. P.; Ventura, O. S.; Vilar, L. C. Q.

An Algebraic Criterion for the Ultraviolet Finiteness of Quantum Field Theories

Authors

Description

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 $β_g$, stating that if the one-loop order contribution vanishes, then $β_g$ will vanish to all orders of perturbation theory. As a by-product, the special case in which $β_g$ 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.
1+32 pages, LaTeX2e, typos corrected