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<p>We study bulk locality constraints in quantum field theories in AdS<sub>2</sub>. The known derivation of locality sum rules in AdS<sub><i>d</i>+1</sub> does not apply for <i>d</i> = 1 due to the different singularity structure of the conformal blocks and the inequivalence of operator orderings on the boundary. Assuming unitarity and a mild growth condition, we establish power-law bounds for correlators, derive dispersion relations and an expansion in terms of “even” and “odd” local blocks that converges in the entire AdS<sub>2</sub>. These yield two novel families of symmetric and antisymmetric locality sum rules. We test these sum rules explicitly in the free scalar field theory.</p>

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Locality constraints in AdS2 without parity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月1日

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  • Manuel Loparco,
  • Grégoire Mathys,
  • João Penedones,
  • Jiaxin Qiao,
  • Xiang Zhao

摘要

We study bulk locality constraints in quantum field theories in AdS2. The known derivation of locality sum rules in AdSd+1 does not apply for d = 1 due to the different singularity structure of the conformal blocks and the inequivalence of operator orderings on the boundary. Assuming unitarity and a mild growth condition, we establish power-law bounds for correlators, derive dispersion relations and an expansion in terms of “even” and “odd” local blocks that converges in the entire AdS2. These yield two novel families of symmetric and antisymmetric locality sum rules. We test these sum rules explicitly in the free scalar field theory.