WdW-patches in AdS${}_3$ and complexity change under conformal transformations II

Abstract

We study the null-boundaries of Wheeler-de Witt (WdW) patches in three dimensional Poincare-AdS, when the selected boundary timeslice is an arbitrary (non-constant) function, presenting some useful analytic statements about them. Special attention will be given to the piecewise smooth nature of the null-boundaries, due to the emergence of caustics and null-null joint curves. This is then applied, in the spirit of our previous paper arXiv:1806.08376, to the problem of how complexity of the CFT${}_2$ groundstate changes under a small local conformal transformation according to the action (CA) proposal. In stark contrast to the volume (CV) proposal, where this change is only proportional to the second order in the infinitesimal expansion parameter $\sigma$, we show that in the CA case we obtain terms of order $\sigma$ and even $\sigma \log (\sigma )$. This has strong implications for the possible field-theory duals of the CA proposal, ruling out an entire class of them.

arXiv comment31 pages + appendices, 9 figures v2: minor improvements, matches published version

References in corpus (77)

• A Stress Tensor for Anti-de Sitter Gravity
• A Covariant Holographic Entanglement Entropy Proposal
• Complexity Equals Action
• A Covariant Entropy Conjecture
• Complexity and Shock Wave Geometries
• Complexity, action, and black holes
• Quantum Computation as Geometry
• Causality & holographic entanglement entropy
• Circuit complexity in quantum field theory
• Towards Complexity for Quantum Field Theory States
• Gravitational action with null boundaries
• A Quantum Focussing Conjecture
• Comments on Holographic Complexity
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Three-dimensional quantum geometry and black holes
• On the Time Dependence of Holographic Complexity
• A 3+1 perspective on null hypersurfaces and isolated horizons
• Noether charge, black hole volume, and complexity
• Complexity of Formation in Holography
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Quantum Computation vs. Firewalls
• Circuit Complexity in Fermionic Field Theory
• Complexity and entanglement for thermofield double states
• Quantum Computation as Gravity
• Circuit complexity for free fermions
• Causal Holographic Information
• A hole-ographic spacetime
• Gravity Dual of Quantum Information Metric
• A Boundary Term for the Gravitational Action with Null Boundaries
• Circuit complexity in interacting QFTs and RG flows
• Holographic Complexity in Vaidya Spacetimes II
• Einstein's Equations from Varying Complexity
• Circuit Complexity for Coherent States
• Path-Integral Complexity for Perturbed CFTs
• Subsystem Complexity and Holography
• Time Evolution of Complexity: A Critique of Three Methods
• Switchbacks and the Bridge to Nowhere
• Black holes, complexity and quantum chaos
• Divergences in Holographic Complexity
• Holographic complexity is nonlocal
• Holographic Holes in Higher Dimensions
• Complexity and the bulk volume, a new York time story
• Holographic Holes and Differential Entropy
• Topological Complexity in AdS3/CFT2
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• Holographic Subregion Complexity from Kinematic Space
• Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game -
• Nuts and Bolts for Creating Space
• A Complexity for Quantum Field Theory States and Application in Thermofield Double States
• Holographic Complexity for Defects Distinguishes Action from Volume
• Strong energy condition and complexity growth bound in holography
• Principles and symmetries of complexity in quantum field theory
• Light Rays, Singularities, and All That
• Subregion Action and Complexity
• Is the gravitational action additive?
• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• Complexity of the AdS Soliton
• A geometric approach to quantum circuit lower bounds
• Divergences in the rate of complexification
• A complexity/fidelity susceptibility g-theorem for AdS${}_3$/BCFT${}_2$
• On 3d Bulk Geometry of Virasoro Coadjoint Orbits: Orbit invariant charges and Virasoro hair on locally AdS3 geometries
• Boundary and Corner Terms in the Action for General Relativity
• Far from equilibrium energy flow in quantum critical systems
• Time evolution of entanglement for holographic steady state formation
• More on complexity of operators in quantum field theory
• Thoughts on Holographic Complexity and its Basis-dependence
• Excitation Entanglement Entropy in 2d Conformal Field Theories
• On Quantization of AdS3 Gravity I: Semi-Classical Analysis
• Butterflies on the Stretched Horizon
• The Boundary of the Future
• Comparison of holographic and field theoretic complexities by time dependent thermofield double states
• The inside outs of AdS(3)/CFT(2): Exact AdS wormholes with entangled CFT duals
• Complexity-action of subregions with corners
• Complexity of operators generated by quantum mechanical Hamiltonians
• Cayley graphs and complexity geometry
• Holographic complexity under a global quantum quench
• Is volume the holographic dual of fidelity susceptibility?

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• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• The First Law of Complexity
• Geometry of Complexity in Conformal Field Theory
• Renormalized Circuit Complexity
• Complexity measures from geometric actions on Virasoro and Kac-Moody orbits
• Cosmological Complexity
• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• Aspects of The First Law of Complexity
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• Quantum complexity in gravity, quantum field theory, and quantum information science
• Time evolution of the complexity in chaotic systems: concrete examples
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• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
• On volume subregion complexity in Vaidya spacetime
• On the Role of Counterterms in Holographic Complexity
• On subregion action complexity in AdS${}_3$ and in the BTZ black hole
• Time dependence of complexity for Lovelock black holes
• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• The first law of differential entropy and holographic complexity
• Stringy Effects and the Role of the Singularity in Holographic Complexity
• To be unitary-invariant or not?: a simple but non-trivial proposal for the complexity between states in quantum mechanics/field theory
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