In this article we present an analysis of the gauge invariance of the technifermion condensate and critical coupling determined from the gap equation to $O\left({\alpha }^2\right)$ in the static limit of walking technicolor. This is an extension of a previous work in which the proof of gauge invariance was restricted to $\xi =2\mathrm{}$ and $\xi =-3\mathrm{}$ gauges. We also briefly discuss how to generalize the proof to $O\left({\alpha }^3\right)$ and higher where $\beta \left(\alpha \right)$ cannot be set equal to zero for arbitrary values of $\alpha$.

• Received 29 April 1991

DOI:https://doi.org/10.1103/PhysRevD.45.1405