On the renormalisability of gauge invariant extensions of the squared gauge potential

Abstract

We show that gauge invariant extensions of the local functional $\cO = \frac12\int d^4x A^2$ have long range non localities which can only be ``renormalised'' with reference to a specific gauge. Consequently, there is no gauge independent way of claiming the perturbative renormalisability of these extensions. In particular, they are not renormalisable in the modern sense of Weinberg and Gomis. Critically, our study does not support the view that ghost fields play an indispensable role in the extension of a local operator into a non-local one as claimed recently in the literature.

arXiv comment1+13 pages. Revised version. New title and abstract. Extended introduction and several sentences have been inserted. Final version to appear in Physics Letters B

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Cited by in corpus (3)

• The influence of the Gribov copies on the gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge
• Interpolating among the Landau, Coulomb and maximal Abelian gauges
• The Non-Local Massive Yang-Mills Action as a Gauged Sigma Model