Phase structure of the twisted SU(3)/U(1)2 flag sigma model on \u211d \xd7 S1

Abstract

We investigate the phase structure of the compactified 2-dimensional nonlinear SU(3)/U(1)2 flag sigma model with respect to two θ-terms. Based on the circle compactification with the ℤ3-twisted boundary condition, which preserves an ’t Hooft anomaly of the original uncompactified theory, we perform the semiclassical analysis based on the dilute instanton gas approximation (DIGA). We clarify classical vacua of the theory and derive fractional instanton solutions connecting these vacua. The resulting phase structure based on DIGA exhibits the quantum phase transitions and triple degeneracy at special points in the (θ1, θ2)-plane, which is consistent with the phase diagram obtained from the anomaly matching and global inconsistency conditions. This result indicates the adiabatic continuity between the flag sigma models on ℝ2 and ℝ × S1 with small compactification radius. We further estimate contributions from instanton-anti-instanton configuration (bion) and show the existence of the imaginary ambiguity, which is expected to be cancelled by that of the perturbative Borel resummation.