PoS - Proceedings of Science
Volume 363 - 37th International Symposium on Lattice Field Theory (LATTICE2019) - Main session
Lattice study on the twisted ${\mathbb C} P^{N-1}$ models on ${\mathbb R} \times S^1$
T. Misumi,* T. Fujimori, E. Itou, M. Nitta, N. Sakai
*corresponding author
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Pre-published on: January 03, 2020
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We report the results of the lattice simulation of the ${\mathbb C} P^{N-1}$ sigma model
on $S_{s}^{1}$(large) $\times$ $S_{\tau}^{1}$(small). We take a sufficiently large ratio of the circumferences to approximate the model on ${\mathbb R} \times S^1$. For periodic boundary condition imposed in the $S_{\tau}^{1}$ 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 ${\mathbb Z}_{N}$ twisted boundary condition, we find that, even at relatively high $\beta$ (small circumference), the regular $N$-sided polygon-shaped distributions of Polyakov loop leads to small expectation values of Polyakov loop, which implies unbroken ${\mathbb Z}_{N}$ 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 $S_{s}^{1}$ direction, which causes transition between ${\mathbb Z}_{N}$ vacua.
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