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<p>We show that various <i>dynamical</i> gauge theories in two, three and four dimensions, obtained as <i>Manin</i> deformations of topological Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) theories, are equivalent to gravitational theories. Since gravity is topological in two and three dimension, this equivalence requires a diffeomorphism breaking background source term. In four dimensions, however, the MacDowell-Mansouri formulation of Einstein gravity with a cosmological constant is obtained identically via the Manin deformation of a particular AKSZ theory.</p>

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Gravity from AKSZ-Manin theories in two, three, and four dimensions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月9日

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  • Leron Borsten,
  • Dimitri Kanakaris,
  • Hyungrok Kim

摘要

We show that various dynamical gauge theories in two, three and four dimensions, obtained as Manin deformations of topological Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) theories, are equivalent to gravitational theories. Since gravity is topological in two and three dimension, this equivalence requires a diffeomorphism breaking background source term. In four dimensions, however, the MacDowell-Mansouri formulation of Einstein gravity with a cosmological constant is obtained identically via the Manin deformation of a particular AKSZ theory.