Lattice Study of the Massive Schwinger Model with a $\theta$ term under L\"uscher's "Admissibility" condition

TL;DR

This study numerically investigates the massive two-flavor QED in 2D with L"uscher's admissibility condition, exploring topological sectors and $ heta$ vacuum effects, and confirms continuum analytic results for meson masses.

Contribution

It introduces a new method to sum over topological sectors under L"uscher's admissibility condition and applies it to analyze $ heta$ vacuum effects in 2D QED.

Findings

Admissibility condition prevents topology changes in HMC simulations.

Configurations in each topological sector can be generated separately.

Meson masses depend on fermion mass and $ heta$, matching continuum theory predictions.

Abstract

We present a numerical study of the massive two-flavor QED in two dimensions with the gauge action proposed by L\"uscher, which allows only ``admissible'' gauge fields. We find that the admissibility condition does not allow any topology changes by the local updation in Hybrid Monte Carlo algorithm so that the configurations in each topological sector can be generated separately. By developing a new method to sum over different topological sectors, we investigate $\theta$ vacuum effects. Combining with domain-wall fermion action, we obtain the fermion mass dependence and $\theta$ dependence of the meson masses, which are consistent with the analytic results by mass perturbation in the continuum theory.