Relationships Between Exact RGs and some Comments on Asymptotic Safety

Understand

The standard flow equation for the effective average action can be derived from a Legendre transform of Polchinski's exact renormalization group equation.

• However, the latter is not well adapted for finding fixed-points with non-zero anomalous dimension.
• Instead, it is more convenient to use a modified version which ensures that the redundant coupling associated with the normalization of the field never appears in the action.
• Taking this as the starting point, a Legendre transform is constructed allowing a direct derivation of the corresponding flow equation for the effective average action.