Gauge-independent transition separating confinement-Higgs phase in the lattice SU(2) gauge-fundamental scalar model

Ryu Ikeda, Seikou Kato, Kei-Ichi Kondo, Akihiro Shibata
High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th)
CHIBA-EP-259, KEK Preprint 2023-27
2023-08-24 16:00:00
According to the conventional studies, the lattice SU(2) gauge-scalar model with a single scalar field in the fundamental representation of the gauge group has a single confinement-Higgs phase where Confinement and Higgs regions are subregions of an analytically continued single phase and there are no thermodynamic phase transitions, which is a well-known consequence of the Osterwalder-Seiler-Fradkin-Shenker theorem. In this paper, however, we show that we can define new type of gauge-invariant operators by combining the original fundamental scalar field and the so-called color-direction field which is obtained by change of field variables based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. By performing the numerical simulations on the lattice without any gauge fixing, we find a new transition line detected by the new gauge-invariant operators which completely separate the confinement-Higgs phase into two parts, confinement phase and the Higgs phase, in the strong gauge coupling, while it agrees with the conventional thermodynamic transition line in the weak gauge coupling. All results are obtained in the gauge-independent way, since no gauge fixing has been imposed in the numerical simulations. Moreover, we give a physical interpretation for the new transition from the viewpoint of the realization of a global symmetry.
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