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Does Complexity Equal Anything?

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We introduce new gravitational observables in anti-de Sitter space that exhibit universal behavior for the thermofield-double state. These observables offer new insights into quantum complexity and the switchback effect in quantum gravity.

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Area of Science:

  • Theoretical physics
  • Quantum gravity
  • Holography

Background:

  • Anti-de Sitter (AdS) space is a key concept in holographic duality.
  • Gravitational observables are crucial for understanding quantum gravity.
  • The thermofield-double state is a fundamental tool in studying quantum entanglement and thermalization in holographic systems.

Purpose of the Study:

  • To introduce a new infinite class of gravitational observables in asymptotically anti-de Sitter space.
  • To investigate the behavior of these observables in the thermofield-double state.
  • To explore their potential as gravitational duals for quantum complexity.

Main Methods:

  • Defining gravitational observables on codimension-one slices in AdS geometry.
  • Analyzing the late-time behavior of these observables for the thermofield-double state.
  • Comparing their properties to known phenomena like the switchback effect.

Main Results:

  • An infinite class of gravitational observables was identified.
  • These observables exhibit linear growth in time at late times for the thermofield-double state.
  • The switchback effect in shock wave geometries was reproduced by these observables.

Conclusions:

  • The newly identified gravitational observables provide universal features in holographic systems.
  • Any observable from this class is a viable candidate for a gravitational dual of quantum complexity.
  • This work deepens the understanding of the connection between gravity and quantum information in AdS/CFT correspondence.