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<p>The Cardy-Rabinovici model is a toy model of the lattice U(1) gauge theories to study various oblique confinement states associated with the nonzero <i>θ</i> angles. We reformulate the 2d version of this model using the modified Villain lattice formalism, and we establish the exact <i>θ</i> periodicity for the Witten effect and the strong-weak duality at the finite lattice spacings. We then study the phase structure of this model based on the duality, symmetry and anomaly, and the perturbative renormalization group.</p>

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2d Cardy-Rabinovici model with the modified Villain lattice: exact dualities and symmetries

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月4日

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  • Nagare Katayama,
  • Yuya Tanizaki

摘要

The Cardy-Rabinovici model is a toy model of the lattice U(1) gauge theories to study various oblique confinement states associated with the nonzero θ angles. We reformulate the 2d version of this model using the modified Villain lattice formalism, and we establish the exact θ periodicity for the Witten effect and the strong-weak duality at the finite lattice spacings. We then study the phase structure of this model based on the duality, symmetry and anomaly, and the perturbative renormalization group.