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We explore quantum information metrics in conformal field theories under operator perturbations. Its gravity dual is approximated by maximal time slice volume in anti-de Sitter spacetime for marginal perturbations.

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Area of Science:

  • Quantum Information Theory
  • High Energy Physics
  • String Theory

Background:

  • Conformal field theories (CFTs) are crucial in understanding critical phenomena and quantum gravity.
  • Quantum information metrics quantify the sensitivity of quantum states to perturbations.
  • The AdS/CFT correspondence relates CFTs to gravitational theories in anti-de Sitter (AdS) spacetime.

Purpose of the Study:

  • To investigate the relationship between quantum information metrics in CFTs and their gravitational duals.
  • To determine the holographic description of fidelity susceptibility under operator perturbations in CFTs.

Main Methods:

  • Perturbation theory is applied to a quantum information metric (fidelity susceptibility) in CFTs.
  • The study analyzes the behavior of this metric with respect to small perturbations by primary operators.
  • The holographic dual is investigated using geometric quantities in anti-de Sitter spacetime.

Main Results:

  • A connection is established between the quantum information metric in CFTs and the volume of a maximal time slice in AdS spacetime.
  • This holographic correspondence is shown to be approximately valid when the perturbation is exactly marginal.
  • The findings are validated through several specific examples.

Conclusions:

  • The volume of a maximal time slice in AdS spacetime serves as a holographic dual for the fidelity susceptibility in CFTs under certain conditions.
  • This provides a geometric interpretation of quantum information measures in the context of holography.
  • The results offer insights into the interplay between quantum information and quantum gravity.