We report the results of the lattice simulation of the CPN−1 sigma model on Ss1(large) × Sτ1 (small). We take a sufficiently large ratio of the circumferences to approximate the model on R × S1. For periodic boundary condition imposed in the Sτ1 direction, we show that the expectation value of the Polyakov loop undergoes a deconfinement crossover as the compactified circumference is decreased, where the peak of the associated susceptibility gets sharper for larger N. For ZN twisted boundary condition, we find that, even at relatively high β (small circumference), the regular N-sided polygon-shaped distributions of Polyakov loop leads to small expectation values of Polyakov loop, which implies unbroken ZN symmetry if sufficient statistics and large volumes are adopted. We also argue the existence of fractional instantons and bions by investigating the dependence of the Polyakov loop on Ss1 direction, which causes transition between ZN vacua.
|ジャーナル||Proceedings of Science|
|出版ステータス||Published - 2019|
|イベント||37th International Symposium on Lattice Field Theory, LATTICE 2019 - Wuhan, China|
継続期間: 2019 6 16 → 2019 6 22
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