2-3 pm: Schemes, gauges and the conformal window

Title: Schemes, gauges and the conformal window

Abstract: A general overview of the basic concepts of renormalization is given in the context of a cubic scalar theory. This naturally leads to a variety of renormalization schemes in non-abelian gauge theories that are used in several applications. These schemes are not restricted to the canonical linear covariant gauge. In addition the implications for the Curci-Ferrari gauge, which is a nonlinear covariant gauge, will be considered. Four and five loop results are presented. Computations in the latter gauge benefit from particular properties of the gauge's Slavnov-Taylor identities which could prove useful in determining high loop order beta-functions. The overall work is placed in the framework of studying the conformal window of QCD. Specifically the flow plane of the gauge coupling and gauge parameter is illustrated at high order thereby consolidating the Shirkov-Tarasov observation that the gauge parameter can be treated as a second coupling constant. The fact that the Banks-Zaks fixed point is a saddle point, but has a mirror infrared stable fixed point for a non-zero critical value of the gauge parameter, is confirmed to five loops. The same critical gauge parameter value had already been noted at various times as being significant in several infrared phenomenology studies. The four loop behaviour of the baryon operator critical exponent in the conformal window is provided as an example.