Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$

Abstract

Using the volume proposal, we compute the change of complexity of holographic states caused by a small conformal transformation in AdS${}_3$/CFT${}_2$. This computation is done perturbatively to second order. We give a general result and discuss some of its properties. As operators generating such conformal transformations can be explicitly constructed in CFT terms, these results allow for a comparison between holographic methods of defining and computing computational complexity and purely field-theoretic proposals. A comparison of our results to one such proposal is given.

arXiv commentv2: 23 pages, 5 figures, added references and one entirely new section about a comparison to a field theory proposal v3: 27 pages, 5 figures, minor improvements. Matches published version

References in corpus (61)

• A Stress Tensor for Anti-de Sitter Gravity
• Complexity Equals Action
• Complexity and Shock Wave Geometries
• Complexity, action, and black holes
• Quantum Computation as Geometry
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Circuit complexity in quantum field theory
• Towards Complexity for Quantum Field Theory States
• Gravitational action with null boundaries
• The Second Law of Quantum Complexity
• Comments on Holographic Complexity
• A Dilatonic Deformation of AdS_5 and its Field Theory Dual
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• On the Time Dependence of Holographic Complexity
• Three-dimensional quantum geometry and black holes
• Holographic 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
• Gravity Dual of Quantum Information Metric
• Einstein's Equations from Varying Complexity
• Subsystem Complexity and Holography
• On Volumes of Subregions in Holography and Complexity
• Path-Integral Complexity for Perturbed CFTs
• Black holes, complexity and quantum chaos
• Three dimensional Janus and time-dependent black holes
• Holographic complexity is nonlocal
• Complexity and the bulk volume, a new York time story
• Topological Complexity in AdS3/CFT2
• Holographic Subregion Complexity from Kinematic Space
• A Complexity for Quantum Field Theory States and Application in Thermofield Double States
• Evolution of Complexity Following a Global Quench
• Strong energy condition and complexity growth bound in holography
• Principles and symmetries of complexity in quantum field theory
• Complexity of the AdS Soliton
• A geometric approach to quantum circuit lower bounds
• Connecting Fisher information to bulk entanglement in holography
• Divergences in the rate of complexification
• Complexity is Simple
• A complexity/fidelity susceptibility g-theorem for AdS${}_3$/BCFT${}_2$
• Fidelity Susceptibility as Holographic PV-Criticality
• On 3d Bulk Geometry of Virasoro Coadjoint Orbits: Orbit invariant charges and Virasoro hair on locally AdS3 geometries
• Holographic local quench and effective complexity
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Far from equilibrium energy flow in quantum critical systems
• On complexity growth in massive gravity theories, the effects of chirality and more
• Time evolution of entanglement for holographic steady state formation
• Generalized fidelity susceptibility at phase transitions
• More on complexity of operators in quantum field theory
• Thoughts on Holographic Complexity and its Basis-dependence
• Berry Phases on Virasoro Orbits
• Information metric and Euclidean Janus correspondence
• Excitation Entanglement Entropy in 2d Conformal Field Theories
• On Complexity Growth in Minimal Massive 3D Gravity
• On Quantization of AdS3 Gravity I: Semi-Classical Analysis
• Holographic Computations of the Quantum Information Metric
• On subregion holographic complexity and renormalization group flows
• The inside outs of AdS(3)/CFT(2): Exact AdS wormholes with entangled CFT duals
• Geons and the Quantum Information Metric
• Bulk Connectedness and Boundary Entanglement

Cited by in corpus (43)

• Quantum Computation as Gravity
• Circuit complexity in interacting QFTs and RG flows
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Time Evolution of Complexity: A Critique of Three Methods
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• 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
• Aspects of The First Law of Complexity
• Conformal field theory complexity from Euler-Arnold equations
• Circuit Complexity From Cosmological Islands
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Holographic Duals of Inhomogeneous Systems: The Rainbow Chain and the Sine-Square Deformation Model
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Time evolution of the complexity in chaotic systems: concrete examples
• Circuit Complexity as a novel probe of Quantum Entanglement: A study with Black Hole Gas in arbitrary dimensions
• Information geometry in quantum field theory: lessons from simple examples
• Exact Gravity Duals for Simple Quantum Circuits
• General Bounds on Holographic Complexity
• Complexity growth rate during phase transitions
• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
• On volume subregion complexity in Vaidya spacetime
• On subregion action complexity in AdS${}_3$ and in the BTZ black hole
• A Generalized Momentum/Complexity Correspondence
• Time dependence of complexity for Lovelock black holes
• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• 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
• Holographic complexity of rotating black holes with conical deficits
• Weighting gates in circuit complexity and holography
• Quasinormal Modes and the Switchback Effect in Schwarzschild-de Sitter
• Causality Constraint on Circuit Complexity from $COSMOEFT$
• Complexity of Scalar Collapse in Anti-de Sitter Spacetime
• Complexity Growth of Dyonic Black holes with Quartic Field Strength Corrections
• What kind of "complexity" is dual to holographic complexity?
• Holographic and QFT Complexity with angular momentum
• Complexity of Magnetization and Magnetic Simplification
• Developments in non-relativistic field theory and complexity
• Cost of holographic path integrals