nPI Resummation in 3D SU(N) Higgs Theory

TL;DR

This paper applies the nPI formalism to analyze the phase diagram of 3D SU(N) Higgs theory, finding qualitative agreement with lattice results but facing challenges in gauge fixing and large-VEV regions.

Contribution

It demonstrates the application of the nPI formalism to nonperturbative gauge theory dynamics and discusses its successes and limitations in capturing phase structure.

Findings

Identification of a first order phase transition with a critical endpoint

Qualitative agreement of critical endpoint location with lattice results

Challenges in gauge fixing and large-VEV region handling

Abstract

We test the utility of the nPI formalism for solving nonperturbative dynamics of gauge theories by applying it to study the phase diagram of SU(N) Higgs theory in 3 Euclidean spacetime dimensions. Solutions reveal standard signatures of a first order phase transition with a critical endpoint leading to a crossover regime, in qualitative agreement with lattice studies. The location of the critical endpoint, x sim 0.14 for SU(2) with a fundamental Higgs, is in rough but not tight quantitative agreement with the lattice. We end by commenting on the overall effectiveness and limitations of an nPI effective action based study. In particular, we have been unable to find an nPI gauge-fixing procedure which can simultaneously display the right phase structure and correctly handle the large-VEV Higgs region. We explain why doing so appears to be a serious challenge.