Does Complexity Equal Anything?

Nov 3, 2021
7 pages
Published in:
  • Phys.Rev.Lett. 128 (2022) 8, 081602
  • Published: Feb 23, 2022
e-Print:
Report number:
  • CERN-TH-2021-181,
  • YITP-22-02

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Abstract: (APS)
We present a new infinite class of gravitational observables in asymptotically Anti-de Sitter space living on codimension-one slices of the geometry, the most famous of which is the volume of the maximal slice. We show that these observables display universal features for the thermofield-double state: they grow linearly in time at late times and reproduce the switch-back effect in shock wave geometries. We argue that any member of this class of observables is an equally viable candidate as the extremal volume for a gravitational dual of complexity.
Note:
  • 6 pages + appendices, 3 figures; v2 minor edits and title change - version as in PRL
  • gravitation: duality
  • space: anti-de Sitter
  • horizon: geometry
  • black hole
  • field theory: conformal
  • holography
  • diffeomorphism: invariance