3-loop 3PI effective action for 3D SU(3) QCD

Understand

The 3PI method is a technique to resum an infinite class of diagrams, which may be useful in studying nonperturbative thermodynamics and dynamics in quantum field theory.

• But it has never been successfully applied to gauge theories, where there are serious questions about gauge invariance breaking.
• We show how to perform the 3PI resummation of QCD in 3 Euclidean spacetime dimensions, a warmup problem to the 4 or 3+1 dimensional case.
• We present the complete details of the technical problems and how they are overcome.