Lattice study of SU(2) gauge theory coupled to four adjoint Higgs fields

TL;DR

This study investigates the phase diagram of an SU(2) gauge theory with four adjoint Higgs fields on a lattice, revealing multiple broken phases and deconfinement transitions relevant to condensed matter and particle physics.

Contribution

First lattice simulation of an SU(2) gauge theory with four adjoint scalar fields, confirming multiple broken phases and analyzing confinement properties.

Findings

Multiple broken phases with different symmetry breaking patterns.

Both phases exhibit deconfinement in studied volume ranges.

Distinct Polyakov loop behaviors characterize the phases.

Abstract

Gauge theories with matter fields in various representations play an important role in different branches of physics. Recently, it was proposed that several aspects of the interesting pseudogap phase of cuprate superconductors near optimal doping may be explained by an emergent $SU(2)$ gauge symmetry. Around the transition with positive hole-doping, one can construct a $(2+1)-$dimensional $SU(2)$ gauge theory coupled to four adjoint scalar fields which gives rise to a rich phase diagram with a myriad of phases having different broken symmetries. We study the phase diagram of this model on the Euclidean lattice using the Hybrid Monte Carlo algorithm. We find the existence of multiple broken phases as predicted by previous mean field studies. Depending on the quartic couplings, the $SU(2)$ gauge symmetry is broken down either to $U(1)$ or $\mathbb{Z}_2$ in the perturbative description of the model. We further study the confinement-deconfinement transition in this theory, and find that both the broken phases are deconfining in the range of volumes that we studied. However, there exists a marked difference in the behavior of the Polyakov loop between the two phases.