TY - JOUR

T1 - Lattice study on the twisted CPN−1 models on R×S1

AU - Misumi, Tatsuhiro

AU - Fujimori, Toshiaki

AU - Itou, Etsuko

AU - Nitta, Muneto

AU - Sakai, Norisuke

N1 - Funding Information:
∗This work is supported by MEXT-Supported Program “Topological Science" S1511006 and by JSPS KAKENHI 18H01217, 19K03875, 18K03627, 19K03817, 16H03984, 15H05855. Numerical simulations were performed on SX-ACE, Osaka University and TSC, Keio University. †Speaker.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

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M3 - Conference article

AN - SCOPUS:85099571613

VL - 363

JO - Proceedings of Science

JF - Proceedings of Science

SN - 1824-8039

M1 - 015

T2 - 37th International Symposium on Lattice Field Theory, LATTICE 2019

Y2 - 16 June 2019 through 22 June 2019

ER -