(Non) Gauge Invariance of Wilsonian Effective Actions in (Supersymmetric) Gauge Theories : A Critical Discussion

Understand

We give a detailed critical discussion of the properties of Wilsonian effective actions, defined by integrating out all modes above a given scale $\mu$.

• In particular, we provide a precise and relatively convenient prescription how to implement the infrared cutoff $\mu$ in any loop integral that is manifestly Lorentz invariant and also preserves global linear symmetries such as e.g.
• supersymmetry.
• We discuss the issue of gauge invariance of effective actions in general and in particular when using background field gauge.