Abstract
We test the utility of the 2PI 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 ∼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 a 2PI (or in general nPI) effective action based study. In particular, we have been unable to find a 2PI 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.
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Abraao York, M.C., Moore, G.D. 2PI resummation in 3D SU(N ) Higgs theory. J. High Energ. Phys. 2014, 105 (2014). https://doi.org/10.1007/JHEP10(2014)105
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DOI: https://doi.org/10.1007/JHEP10(2014)105