Lattice study of the massive Schwinger model with a $\theta$ term under Lüscher’s “admissibility” condition

Lüscher’s “admissibility” condition on the gauge field space plays an essential role in constructing lattice gauge theories which have exact chiral symmetries. We apply the gauge action proposed by Lüscher with the domain-wall fermion action to the numerical simulation of the massive Schwinger model. We find this action can generate configurations in each topological sector separately without any topology changes. By developing a new method to sum over different topological sectors, we calculate the meson masses in the nonzero $\theta$ vacuum.