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<p>We find infinitely many soliton-like solutions in a deformation of the sine-Gordon theory in (<i>d</i> + 1)-dimensional AdS<sub><i>d</i>+1</sub> (anti-de Sitter) spacetime for <i>d</i> ≥ 2, as well as single solitonic solutions in dS<sub><i>d</i>+1</sub> (de Sitter) and H<sub><i>d</i>+1</sub> (Lobachevsky) spaces for <i>d</i> ≥ 1 and in AdS<sub>2</sub>. We also find a deformation of the kink solution in scalar field theory with a polynomial potential in AdS<sub>2</sub>. The deformation of the theories are due to a coupling of the fields to the curvature of the background space-time. In the infinite radius limit, single soliton solutions reduce to solitons in flat space. Meanwhile, the multisoliton solution in AdS<sub><i>d</i>+1</sub> for <i>d</i> ≥ 2 for certain values of the parameters reduces in the same limit to a single soliton solution boosted in the normal direction. However, there are also multisoliton solutions in AdS<sub><i>d</i>+1</sub> for <i>d</i> ≥ 2 that do not have a flat space limit. In all cases we consider, gravity is not dynamical, and the background space remains strictly equal to either AdS<sub><i>d</i>+1</sub>, dS<sub><i>d</i>+1</sub>, or H<sub><i>d</i>+1</sub>, respectively.</p>

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Sine-Gordon solitons in AdS, dS and other hyperbolic spaces

  • 期刊论文

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  • 发表日期：

    2026年7月29日

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  • E. T. Akhmedov,
  • D. V. Diakonov

摘要

We find infinitely many soliton-like solutions in a deformation of the sine-Gordon theory in (d + 1)-dimensional AdSd+1 (anti-de Sitter) spacetime for d ≥ 2, as well as single solitonic solutions in dSd+1 (de Sitter) and Hd+1 (Lobachevsky) spaces for d ≥ 1 and in AdS2. We also find a deformation of the kink solution in scalar field theory with a polynomial potential in AdS2. The deformation of the theories are due to a coupling of the fields to the curvature of the background space-time. In the infinite radius limit, single soliton solutions reduce to solitons in flat space. Meanwhile, the multisoliton solution in AdSd+1 for d ≥ 2 for certain values of the parameters reduces in the same limit to a single soliton solution boosted in the normal direction. However, there are also multisoliton solutions in AdSd+1 for d ≥ 2 that do not have a flat space limit. In all cases we consider, gravity is not dynamical, and the background space remains strictly equal to either AdSd+1, dSd+1, or Hd+1, respectively.