Complexity and Boost Symmetry

Abstract

We find that the time dependence of holographic complexity is controlled by the Rindler boost symmetry across the horizon. By studying the collision energy experienced by an infalling object, we see the breaking of this boost symmetry is closely related to firewalls, which in turn shows the connection between the time dependence of complexity and firewalls. We further identify the black and white hole interiors as two tapes storing different parts of the minimal circuit preparing the state. Depending on whether the quantum gates are being laid on the tape at a particular moment, each tape can be in two states: working, or locked. We interpret the existence of firewalls as the locking of tapes.

28 pages, 27 figures

References in corpus (4)

• Complexity and Shock Wave Geometries
• Gravitational action with null boundaries
• Quantum Complexity and Negative Curvature
• Switchbacks and the Bridge to Nowhere

Cited by in corpus (19)

• Complexity and entanglement for thermofield double states
• Circuit complexity in interacting QFTs and RG flows
• Time Evolution of Complexity: A Critique of Three Methods
• Holographic Complexity for Defects Distinguishes Action from Volume
• Complexity of AdS_5 black holes with a rotating string
• Complexity and Momentum
• Complexity growth of rotating black holes with a probe string
• Evolution of Holographic Complexity Near Critical Point
• A quantum circuit interpretation of evaporating black hole geometry
• Holographic Complexity Bounds
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• On Volume Subregion Complexity in Non-Conformal Theories
• Action Growth of Dyonic Black Holes and Electromagnetic Duality
• Horizons Protect Church-Turing
• Weighting gates in circuit complexity and holography
• Causality Constraint on Circuit Complexity from $COSMOEFT$
• On Complexity of Holographic Flavors
• Switchback effect of holographic complexity in multiple-horizon black holes
• Probe strings on AdS accelerating black holes