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

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 pseudogap phase of cuprate superconductors near optimal doping may be explained by an emergent <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mtext>SU</a:mtext><a:mo>(</a:mo><a:mn>2</a:mn><a:mo>)</a:mo></a:mrow></a:math> gauge symmetry. Around the transition with positive hole doping, one can construct a <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>(</b:mo><b:mn>2</b:mn><b:mo>+</b:mo><b:mn>1</b:mn><b:mo>)</b:mo><b:mo>−</b:mo></b:mrow><b:mtext>dimensional</b:mtext></b:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi mathvariant="double-struck">Z</c:mi><c:mn>2</c:mn></c:msub></c:math> 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. Published by the American Physical Society 2024