3-loop 3PI effective action for 3D SU(3) QCD
Mark C. Abraao York, Guy D. Moore, Marcus Tassler
TL;DR
This paper develops a 3-loop 3PI effective action approach for 3D SU(3) QCD, addressing technical challenges and laying groundwork for nonperturbative studies in gauge theories.
Contribution
It demonstrates the first successful application of the 3PI resummation method to a gauge theory, specifically 3D SU(3) QCD, overcoming gauge invariance issues.
Findings
Completed the 3-loop 3PI resummation for 3D SU(3) QCD
Detailed the technical solutions to gauge invariance problems
Set the stage for future comparison with lattice results
Abstract
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. We postpone a comparison of gauge invariant correlation functions with their lattice-determined counterparts to a future publication.
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