AdlerBardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories
Abstract
We prove the AdlerBardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, local Lorentz symmetry, and Abelian and nonAbelian YangMills symmetries, and that the local functionals of vanishing ghost numbers satisfy a variant of the KlubergSternZuber conjecture. We show that if the gauge anomalies are trivial at one loop, for every truncation of the theory there exists a subtraction scheme where they manifestly vanish to all orders, within the truncation. Outside the truncation the cancellation of gauge anomalies can be enforced by finetuning local counterterms. The framework of the proof is worked out by combining a recently formulated chiral dimensional regularization with a gauge invariant higherderivative regularization. If the higherderivative regularizing terms are placed well beyond the truncation, and the energy scale Λ associated with them is kept fixed, the theory is superrenormalizable and has the property that, once the gauge anomalies are canceled at one loop, they manifestly vanish from two loops onwards by simple power counting. When the Λ divergences are subtracted away and Λ is sent to infinity, the anomaly cancellation survives in a manifest form within the truncation and in a nonmanifest form outside. The standard model coupled to quantum gravity satisfies all the assumptions, so it is free of gauge anomalies to all orders.
 Publication:

Physical Review D
 Pub Date:
 May 2015
 DOI:
 10.1103/PhysRevD.91.105016
 arXiv:
 arXiv:1501.07014
 Bibcode:
 2015PhRvD..91j5016A
 Keywords:

 11.10.Gh;
 03.70.+k;
 04.60.m;
 11.15.q;
 Renormalization;
 Theory of quantized fields;
 Quantum gravity;
 Gauge field theories;
 High Energy Physics  Theory;
 High Energy Physics  Phenomenology;
 Mathematical Physics
 EPrint:
 63 pages