An Algebraic Criterion for the Ultraviolet Finiteness of Quantum Field Theories

Details An Algebraic Criterion for the Ultraviolet Finiteness of Quantum Field Theories An Algebraic Criterion for the Ultraviolet Finiteness of Quantum Field Theories

2001-03-14

arxiv.org/abs/hep-th/0103110v2

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.

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