A study of the gauge invariant, nonlocal mass operator $Tr \int d^4x F_{\mu\nu}(D^2)^{-1} F_{\mu\nu}$ in Yang-Mills theories

TL;DR

This paper investigates a nonlocal gauge-invariant mass operator in Yang-Mills theories, demonstrating its local reformulation, renormalizability, and calculating its anomalous dimensions, with implications for gauge invariance of condensates.

Contribution

It introduces a local, polynomial form of a nonlocal mass operator in Yang-Mills theories and proves its renormalizability, providing new insights into gauge-invariant mass generation.

Findings

The nonlocal operator can be expressed in local form with additional fields.

The local action is proven to be multiplicatively renormalizable.

One-loop anomalous dimensions of the operator are computed.

Abstract

The nonlocal mass operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ is considered in Yang-Mills theories in Euclidean space-time. It is shown that the operator $Tr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ can be cast in local form through the introduction of a set of additional fields. A local and polynomial action is thus identified. Its multiplicative renormalizability is proven by means of the algebraic renormalization in the class of linear covariant gauges. The anomalous dimensions of the fields and of the mass operator are computed at one loop order. A few remarks on the possible role of this operator for the issue of the gauge invariance of the dimension two condensates are outlined.