Lattice Study of the Massive Schwinger Model with $\theta$ Term under L\"{u}scher's "Admissibility" Condition

TL;DR

This paper explores a lattice approach to the massive Schwinger model using L"uscher's admissibility condition, enabling separate topological sector simulations and accurate meson mass calculations in nonzero-$ heta$ vacua.

Contribution

It introduces a novel lattice gauge action combined with domain-wall fermions that maintains topological sectors separately, facilitating precise $ heta$-vacuum studies.

Findings

Configurations in each topological sector are generated without topology changes.

A new method for summing over topological sectors is developed.

Meson masses are calculated in nonzero-$ heta$ vacuum.

Abstract

L\"uscher's ``admissibility'' condition on the gauge field space plays an essential role in constructing lattice gauge theories which has exact chiral symmetries. We apply the gauge action proposed by L\"uscher 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 meson masses in nonzero-$\theta$ vacuum.