Renormalization group flow equations connected to the $n$PI effective action

Understand

In this paper we derive a hierarchy of integral equations from the 4PI effective action which have the form of Bethe-Salpeter equations.

• We show that the vertex functions defined by these equations can be used to truncate the exact renormalization group flow equations.
• This truncation has the property that the flow is a total derivative with respect to the flow parameter.
• We also show that the truncation is equivalent to solving the $n$PI equations of motion.