Complexity for Conformal Field Theories in General Dimensions

Abstract

We study circuit complexity for conformal field theory states in arbitrary dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group. Different choices of distance functions can be understood in terms of the geometry of coadjoint orbits of the conformal group. We explicitly relate our circuits to timelike geodesics in anti-de Sitter space and the complexity metric to distances between these geodesics. We extend our method to circuits in other symmetry groups using a group theoretic generalization of the notion of coherent states.

arXiv comment5+18 pages, 2 figures; v2: substantial new results about geodesics in the complexity metric and the relation to holography

References in corpus (59)

• Large N Field Theories, String Theory and Gravity
• Ultimate physical limits to computation
• Complexity Equals Action
• Complexity and Shock Wave Geometries
• Complexity, action, and black holes
• Quantum Computation as Geometry
• Quantum critical scaling of the geometric tensors
• Circuit complexity in quantum field theory
• Towards Complexity for Quantum Field Theory States
• Comments on Holographic Complexity
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• On the Time Dependence of Holographic Complexity
• Complexity of Formation in Holography
• Circuit Complexity in Fermionic Field Theory
• A Stereoscopic Look into the Bulk
• Complexity and entanglement for thermofield double states
• Quantum Computation as Gravity
• Circuit complexity for free fermions
• Gravity Dual of Quantum Information Metric
• Circuit complexity in interacting QFTs and RG flows
• Classifying and measuring the geometry of the quantum ground state manifold
• Holographic Complexity in Vaidya Spacetimes II
• Einstein's Equations from Varying Complexity
• Subsystem Complexity and Holography
• Entanglement, Holography and Causal Diamonds
• Recursion Relations for Conformal Blocks
• Holographic Complexity in Vaidya Spacetimes I
• Divergences in Holographic Complexity
• Holographic complexity is nonlocal
• Complexity and the bulk volume, a new York time story
• Integrable Floquet dynamics
• Path integral optimization as circuit complexity
• Holographic Subregion Complexity from Kinematic Space
• The boundary dual of the bulk symplectic form
• Geometry of Complexity in Conformal Field Theory
• Complexity measures from geometric actions on Virasoro and Kac-Moody orbits
• From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
• Holographic Complexity for Defects Distinguishes Action from Volume
• Circuit Complexity across a Topological Phase Transition
• Holographic de Sitter Geometry from Entanglement in Conformal Field Theory
• Conformal field theory complexity from Euler-Arnold equations
• Modular Berry Connection
• A Modular Sewing Kit for Entanglement Wedges
• Complexity in the presence of a boundary
• Does Boundary Distinguish Complexities?
• Berry Phases on Virasoro Orbits
• Liouville Conformal Field Theories in Higher Dimensions
• Charged Complexity and the Thermofield Double State
• Spacetime as a quantum circuit
• Comments on Determinant Formulas for General CFTs
• Kinematic space and the orbit method
• Complexity and Floquet dynamics: non-equilibrium Ising phase transitions
• Holography and the Future Tube
• Vector coherent state representations, induced representations, and geometric quantization: II. Vector coherent state representations
• Coadjoint Orbits, Cocycles and Gravitational Wess-Zumino
• Vector coherent state representations and their inner products
• On particle dynamics in AdS_{N+1} space-time
• Integration of massive states as contractions of non linear $\sigma$-models
• Canonical variables and analysis on so(n,2)

Cited by in corpus (51)

• Quantum chaos and the complexity of spread of states
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Universal chaotic dynamics from Krylov space
• Quantum complexity and topological phases of matter
• Krylov Complexity in Free and Interacting Scalar Field Theories with Bounded Power Spectrum
• Complexity Equals Anything II
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
• Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos
• State Dependence of Krylov Complexity in $2d$ CFTs
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Quantum state complexity meets many-body scars
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Exact Gravity Duals for Simple Quantum Circuits
• Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
• Entanglement and geometry from subalgebras of the Virasoro algebra
• Is Action Complexity better for de Sitter space in Jackiw-Teitelboim gravity?
• The Early Universe as an Open Quantum System: Complexity and Decoherence
• Krylov spread complexity as holographic complexity beyond JT gravity
• Pseudo complexity of purification for free scalar field theories
• Complexity of quantum circuits via sensitivity, magic, and coherence
• Complexity of warped conformal field theory
• On the time dependence of holographic complexity for charged AdS black holes with scalar hair
• Decoherence, Entanglement Negativity and Circuit Complexity for Open Quantum System
• Volume complexity of dS bubbles
• Action complexity in the presence of defects and boundaries
• Circuit Complexity in Topological Quantum Field Theory
• Holographic complexity of Jackiw-Teitelboim gravity from Karch-Randall braneworld
• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• Virasoro Entanglement Berry Phases
• Circuit Complexity for Carrollian Conformal (BMS) Field Theories
• Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• Holographic complexity of rotating black holes with conical deficits
• Negative Complexity of Formation: the Compact Dimensions Strike Back
• Saturation and recurrence of quantum complexity in random local quantum dynamics
• Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function
• The Complexity of Being Entangled
• Towards complexity of primary-deformed Virasoro circuits
• Causality Constraint on Circuit Complexity from $COSMOEFT$
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Complexity for superconformal primaries from BCH techniques
• Random Circuits in the Black Hole Interior
• The landscape of complexity measures in 2D gravity
• Benchmarking quantum chaos from geometric complexity
• Probing the self-coherence of primordial quantum fluctuations with complexity
• Information Geometry and Holographic Correlators
• Toward a physically motivated notion of Gaussian complexity geometry
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Growth of a renormalized operator as a probe of chaos
• Cost of holographic path integrals