Does Complexity Equal Anything?

TL;DR

The paper introduces a new class of gravitational observables in AdS space, demonstrating their universal late-time growth and potential as duals for complexity in holography.

Contribution

It presents an infinite class of observables with universal features, expanding the understanding of gravitational duals for complexity beyond extremal volume.

Findings

Observables grow linearly in time at late times.

They reproduce the switch-back effect in shock wave geometries.

Any member of the class can serve as a candidate for gravitational complexity.

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.