Ward identities and gauge independence in general chiral gauge theories

Abstract

Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible for interesting effects. We prove that gauge invariance always implies gauge independence, which in turn ensures perturbative unitarity. Precisely, we consider potentially anomalous theories that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem. We show that when we make a canonical transformation on the tree-level action, it is always possible to re-renormalize the divergences and re-fine-tune the finite local counterterms, so that the renormalized $\Gamma$ functional of the transformed theory is also free of gauge anomalies, and is related to the renormalized $\Gamma$ functional of the starting theory by a canonical transformation. An unexpected consequence of our results is that the beta functions of the couplings may depend on the gauge-fixing parameters, although the physical quantities remain gauge independent. We discuss nontrivial checks of high-order calculations based on gauge independence and determine how powerful they are.

56 pages; v3: some expanded arguments, more references, PRD version

References in corpus (6)

• Renormalization of Lorentz violating theories
• Three-loop SM beta-functions for matrix Yukawa couplings
• Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard Model
• Weighted power counting and chiral dimensional regularization
• Adler-Bardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories
• Canonical Flow in the Space of Gauge Parameters

Cited by in corpus (6)

• The Ultraviolet Behavior Of Quantum Gravity
• Aspects of perturbative unitarity
• Finite Field-Dependent BRST-antiBRST Transformations: Jacobians and Application to the Standard Model
• Adler-Bardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories
• Background field method and the cohomology of renormalization
• Purely virtual extension of quantum field theory for gauge invariant fields: Yang-Mills theory