Background field method in the gradient flow

Understand

In perturbative consideration of the Yang--Mills gradient flow, it is useful to introduce a gauge non-covariant term ("gauge-fixing term") to the flow equation that gives rise to a Gaussian damping factor also for gauge degrees of freedom.

• In the present paper, we consider a modified form of the gauge-fixing term that manifestly preserves covariance under the background gauge transformation.
• It is shown that our gauge-fixing term does not affect gauge-invariant quantities as the conventional gauge-fixing term.
• The formulation thus allows a background gauge covariant perturbative expansion of the flow equation that provides, in particular, a very efficient computational method of expansion coefficients in the small flow time expansion.