Adler-Bardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories

Abstract

We prove the Adler-Bardeen 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 non-Abelian Yang-Mills symmetries, and that the local functionals of vanishing ghost number satisfy a variant of the Kluberg-Stern--Zuber 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 fine-tuning local counterterms. The framework of the proof is worked out by combining a recently formulated chiral dimensional regularization with a gauge invariant higher-derivative regularization. If the higher-derivative regularizing terms are placed well beyond the truncation, and the energy scale $\Lambda$ associated with them is kept fixed, the theory is super-renormalizable and has the property that, once the gauge anomalies are cancelled at one loop, they manifestly vanish from two loops onwards by simple power counting. When the $\Lambda$ divergences are subtracted away and $\Lambda$ 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.

arXiv comment63 pages; v2: minor changes, PRD version

References in corpus (15)

• Renormalization of Lorentz violating theories
• Local BRST cohomology in Einstein--Yang--Mills theory
• Electric Charge Quantization
• Higher covariant derivative regularization revisited
• Anomalies to All Orders
• Equivalence of Dimensional Reduction and Dimensional Regularisation
• Dimensional Reduction in Non-Supersymmetric Theories
• Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard Model
• Standard Model Without Elementary Scalars And High Energy Lorentz Violation
• Adler-Bardeen theorem and vanishing of the gauge beta function
• Background field method, Batalin-Vilkovisky formalism and parametric completeness of renormalization
• Weighted power counting and chiral dimensional regularization
• Adler-Bardeen theorem and manifest anomaly cancellation to all orders in gauge theories
• Ward identities and gauge independence in general chiral gauge theories
• Refining the anomaly consistency condition

Cited by in corpus (7)

• Universally Finite Gravitational & Gauge Theories
• Aspects of perturbative unitarity
• A Note on Gauge Anomaly Cancellation in Effective Field Theories
• Classical and Quantum Nonlocal Supergravity
• Background field method and the cohomology of renormalization
• Ward identities and gauge independence in general chiral gauge theories
• The unfolded universe of elementary particles. A geometric explanation of the standard model structure