Non-perturbative resummation in three dimensional Yang-Mills theory
Abraao York, C Mark · 2014
An n-particle-irreducible (nPI) effective action Gamma[phi, G, ...] is a functional whose stationary points coincide with the exact Green's functions of a quantum theory (for n=2 this is known as a Phi-derivable approximation). Any practical application would necessitate a truncation of Gamma at some finite loop order; then, the stationary points of Gamma[phi, G, ...] would correspond to a selective resummation to all orders in a perturbative expansion. This thesis explores the application of these functional techniques to non-abelian gauge theory in three spacetime dimensions.3D gauge theories are physically relevant in that they provide an effective description of the non-perturbative sectors of high temperature 4D gauge theories. In this work we focus our attention on two particular 3D models, pure SU(N) Yang-Mills and Yang-Mills coupled to a scalar field. In our study of pure Yang-Mills theory we address the technical and computational challenges associated with the resolution of the three-loop 3PI equations of motion; in the end obtaining solutions for the fully resummed two and three-point functions of the theory. Subsequently, the study of SU(N) Higgs theory is physically motivated, in that this field theory provides a framework which can be used to compute gauge-invariant observables using the nPI method. In determining the phase diagram of SU(N) Higgs theory (specifically in the three-loop 2PI formalism) we address the overall accuracy and applicability of these methods to the non-perturbative study of Yang-Mills theory.