Complexity Growth in Flat Spacetimes

Abstract

We use the complexity equals action proposal to calculate the rate of complexity growth for field theories that are the holographic duals of asymptotically flat spacetimes. To this aim, we evaluate the on-shell action of asymptotically flat spacetime on the Wheeler-DeWitt patch. This results in the same expression as can be found by taking the flat-space limit from the corresponding formula related to the asymptotically AdS spacetimes. For the bulk dimensions that are greater than three, the rate of complexity growth at late times approaches from above to Lloyd's bound. However, for the three-dimensional bulks, this rate is a constant and differs from Lloyd's bound by a logarithmic term.

arXiv comment23 pages, 5 figures, V2: Numeric results corrected, text corrected accordingly, Ref. added V3: Published version

References in corpus (44)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Eternal Black Holes in AdS
• Lecture Notes on Holographic Renormalization
• Ultimate physical limits to computation
• The maximum speed of dynamical evolution
• Complexity Equals Action
• Complexity and Shock Wave Geometries
• Aspects of the BMS/CFT correspondence
• Complexity, action, and black holes
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions
• The BMS/GCA correspondence
• Gravitational action with null boundaries
• Comments on Holographic Complexity
• A New Cosmological Scenario in String Theory
• Holography of 3d Flat Cosmological Horizons
• On the Time Dependence of Holographic Complexity
• Holographic Complexity
• Asymptotic Structure of Symmetry Reduced General Relativity
• xTras: a field-theory inspired xAct package for Mathematica
• Complexity of Formation in Holography
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Complexity Growth for AdS Black Holes
• Entanglement entropy in Galilean conformal field theories and flat holography
• A Boundary Term for the Gravitational Action with Null Boundaries
• Time-dependent Orbifolds and String Cosmology
• Entanglement Entropy in Flat Holography
• No Black Hole Theorem in Three-Dimensional Gravity
• Complexity Growth with Lifshitz Scaling and Hyperscaling Violation
• Holographic Complexity And Cosmological Singularities
• Stress tensor correlators in three-dimensional gravity
• Evolution of Complexity Following a Global Quench
• Strong energy condition and complexity growth bound in holography
• Holographic Entanglement and Poincare blocks in three dimensional flat space
• Wilson Lines and Holographic Entanglement Entropy in Galilean Conformal Field Theories
• Divergences in the rate of complexification
• Gravitational anomalies, entanglement entropy, and flat-space holography
• Comparison of holographic and field theoretic complexities by time dependent thermofield double states
• Aspects of the zero $\Lambda$ limit in the AdS/CFT correspondence
• Holographic Complexity Of Cold Hyperbolic Black Holes
• Flat-Space Holography and Stress Tensor of Kerr Black Hole
• Stress Tensor Correlators of CCFT${}_2$ using Flat-Space Holography
• Logarithmic Correction to BMSFT Entanglement Entropy

Cited by in corpus (13)

• Flat space holography and complex SYK
• Subregion Action and Complexity
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Holographic complexity of anisotropic black branes
• Complexity growth of rotating black holes with a probe string
• Null boundary terms for Lanczos-Lovelock gravity
• Evolution of Holographic Complexity Near Critical Point
• Circuit Complexity for Carrollian Conformal (BMS) Field Theories
• On Volume Subregion Complexity in Non-Conformal Theories
• A note on holographic subregion complexity and QCD phase transition
• Complexity and uncomplexity during energy injection
• Note on stability and holographic subregion complexity
• Probe strings on AdS accelerating black holes