Lattice study on the twisted CP^N−1 models on R×S¹

We report the results of the lattice simulation of the CP^N−1 sigma model on S_s¹(large) × S_τ¹ (small). We take a sufficiently large ratio of the circumferences to approximate the model on R × S¹. For periodic boundary condition imposed in the S_τ¹ 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 Z_N 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 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_s¹ direction, which causes transition between Z_N vacua.