Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model

DOI DOI PDF Web Site 被引用文献17件 参考文献99件 オープンアクセス

書誌事項

公開日
2019-07
資源種別
journal article
権利情報
  • https://creativecommons.org/licenses/by/4.0/
  • https://creativecommons.org/licenses/by/4.0/
DOI
  • 10.1007/jhep07(2019)018
  • 10.48550/arxiv.1905.05781
公開者
Springer Science and Business Media LLC

説明

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title> <jats:p>This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete ’t Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge-<jats:italic>q N</jats:italic>-flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete ’t Hooft anomaly matching to theories on ℝ<jats:sup>2</jats:sup> and its compactification to ℝ× <jats:italic>S</jats:italic> <jats:sub> <jats:italic>L</jats:italic> </jats:sub> <jats:sup>1</jats:sup> . We then compare the ’t Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are <jats:italic>Nq</jats:italic> vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional <jats:italic>θ</jats:italic> dependence e<jats:sup>i<jats:italic>θ</jats:italic>/<jats:italic>Nq</jats:italic> </jats:sup>, which provides the <jats:italic>Nq</jats:italic>-branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by “quantum” instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large-<jats:italic>N</jats:italic> limit of the Schwinger model with twisted boundary conditions satisfy volume independence.</jats:p>

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