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<p>Building on the pioneering work of [1], we propose a holographic description of spread complexity and its rate in 2D CFTs. By exploiting <i>SL</i>(2, <i>ℝ</i>) symmetry, we explicitly construct the Krylov basis, expressing spread complexity as a linear combination of generator expectation values. Within the AdS/CFT correspondence, we translate these boundary expectations directly into bulk kinematic variables. These findings suggest that spread complexity manifests as the energy measured by a bulk observer, with its rate corresponding to the radial momentum.</p>

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The holography of spread complexity. A story of observers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月21日

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  • Zhehan Li,
  • Jia Tian

摘要

Building on the pioneering work of [1], we propose a holographic description of spread complexity and its rate in 2D CFTs. By exploiting SL(2, ℝ) symmetry, we explicitly construct the Krylov basis, expressing spread complexity as a linear combination of generator expectation values. Within the AdS/CFT correspondence, we translate these boundary expectations directly into bulk kinematic variables. These findings suggest that spread complexity manifests as the energy measured by a bulk observer, with its rate corresponding to the radial momentum.