Speaker
Description
In this talk, I will report our recent achievements based on ref. [1].
Quark-Hadron Continuity on QCD and Gauge-Higgs model
A big puzzle of QCD and its phase diagram is whether quark matter at high density and hadronic matter are smoothly connected or separated by the phase transition. On the one hand, since both phases have the same symmetry, the continuity between hadrons and quark matter (quark-hadron continuity) seems to be realized. On the other hand, intuitively, the two phases are distinguished by the presence or absence of the color charge, and the phase transition seems to exist. To settle this issue, the color charge needs to be calculated numerically from nonlocal operators such as the Wilson loop and Aharonov--Bohm phase. We have examined the usefulness of nonlocal operators in analyzing the behavior of the phase transition by using an Abelian Higgs model as a testing ground. This model does not have the sign problem and has the same continuity problem as QCD if the gauge group is extended.
Phase Diagram of Abelian Higgs model
We calculated the Polyakov loop and 't Hooft loop of the charge-2 Abelian Higgs model on the lattice. These nonlocal operators are order parameters of confinement. We confirmed the phase transition lines of the theory and obtained the phase diagram. Furthermore, the Higgs and Coulomb deconfined phases were distinguished.
Aharonov--Bohm Phase on Lattice
We also calculated the Wilson loop and the Aharonov--Bohm phase on the lattice. A vortex of the Higgs field is generated, and several size loops are considered. We found the first-order phase transition on the Wilson loop, but phase values become difficult to read at the confined phase.
[1] Yusuke Shimada and Arata Yamamoto, "Analyzing the Higgs–Confinement Transition with Nonlocal Operators on the Lattice", Progress of Theoretical and Experimental Physics, Volume 2025, Issue 4, April 2025.
