Does Complexity Equal Anything?

Abstract

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.

6 pages + appendices, 3 figures; v2 minor edits and title change - version as in PRL

References in corpus (5)

• Complexity and Shock Wave Geometries
• Gravitational action with null boundaries
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• Entanglement equilibrium for higher order gravity
• General Bounds on Holographic Complexity

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