Q-curvature and Path Integral Complexity

Abstract

We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal field theories in terms of Q-curvature actions. We explore the properties and consequences of these actions from the perspective of the optimization programme, tensor networks and penalty factors. Moreover, in the context of recently proposed holographic path integral optimization, we consider higher curvature contributions on the Hartle-Hawking bulk slice and study their impact on the optimization as well as their relation to Q-curvature actions and finite cut-off holography.

arXiv comment38 pages, 3 figures, typos corrected, references added, published version in JHEP

References in corpus (46)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Stress Tensor for Anti-de Sitter Gravity
• The Holographic Weyl anomaly
• Entanglement renormalization
• Complexity Equals Action
• Complexity and Shock Wave Geometries
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Quantum Computation as Geometry
• Holographic Dual of BCFT
• Aspects of AdS/BCFT
• Tensor Network Renormalization
• The Second Law of Quantum Complexity
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Quantum Computation as Gravity
• Holography at finite cutoff with a $T^2$ deformation
• Quantum Complexity and Negative Curvature
• Einstein's Equations from Varying Complexity
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Path-Integral Complexity for Perturbed CFTs
• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
• The Complexity Geometry of a Single Qubit
• Path integral optimization as circuit complexity
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• Renormalized Circuit Complexity
• Sphere partition functions and cut-off AdS
• From Path Integrals to Tensor Networks for AdS/CFT
• Path Integral Optimization for $T\bar{T}$ Deformation
• New Massive Gravity and AdS_4 counterterms
• Path-Integral Optimization from Hartle-Hawking Wave Function
• Conformal anomaly c-coefficients of superconformal 6d theories
• Liouville Conformal Field Theories in Higher Dimensions
• Holographic Path-Integral Optimization
• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
• Conformal Boundary Conditions from Cutoff AdS${}_3$
• Spacetime as a quantum circuit
• On c-theorems in arbitrary dimensions
• Complexity and Emergence of Warped ${\text{AdS}}_3$ Space-time from Chiral Liouville Action
• Building Tensor Networks for Holographic States
• Emergent Einstein Equation in p-adic CFT Tensor Networks
• Simple recipe for holographic Weyl anomaly
• $Q$-curvature and gravity
• Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities
• Emergent geometry and path integral optimization for a Lifshitz action
• Liouville Conformal Field Theory on even-dimensional spheres

Cited by in corpus (6)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Krylov Complexity in Free and Interacting Scalar Field Theories with Bounded Power Spectrum
• Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos
• Complexity growth of BTZ black hole in massive gravity with a null string
• Quantum fluctuation on the worldsheet of probe string in BTZ black hole
• Cost of holographic path integrals