Complexity and Emergence of Warped ${\text{AdS}}_3$ Space-time from Chiral Liouville Action

Abstract

In this work we explore the complexity path integral optimization process for the case of warped ${\text{AdS}}_3$/warped ${\text{CFT}}_2$ correspondence. We first present the specific renormalization flow equations and analyze the differences with the case of CFT. We discuss how the "chiral Liouville action" could replace the Liouville action as the suitable cost function for this case. Starting from the other side of the story, we also show how the deformed Liouville actions could be derived from the spacelike, timelike and null warped metrics and how the behaviors of boundary topological terms creating these metrics, versus the deformation parameter are consistent with our expectations. As the main results of this work, we develop many holographic tools for the case of warped ${\text{AdS}}_3$, which include the tensor network structure for the chiral warped CFTs, entangler function, surface/state correspondence, quantum circuits of Kac-Moody algebra and kinematic space of WAdS/WCFTs. In addition, we discuss how and why the path-integral complexity should be generalized and propose several other examples such as Polyakov, p-adic strings and Zabrodin actions as the more suitable cost functions to calculate the circuit complexity.

arXiv comment62 pages, 9 figures, v2: references added

References in corpus (74)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Covariant Holographic Entanglement Entropy Proposal
• A Method for Simulating Chiral Fermions on the Lattice
• Complexity Equals Action
• Entanglement Renormalization and Holography
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Circuit complexity in quantum field theory
• Towards Complexity for Quantum Field Theory States
• Warped AdS_3 Black Holes
• Tensor Network Renormalization
• 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
• Constraints on symmetry from holography
• A Stereoscopic Look into the Bulk
• Quantum Computation as Gravity
• Surface/State Correspondence as a Generalized Holography
• On The Entanglement Entropy For Gauge Theories
• A hole-ographic spacetime
• New Boundary Conditions for AdS3
• Aspects of Entanglement Entropy for Gauge Theories
• Dipoles, Twists and Noncommutative Gauge Theory
• Einstein's Equations from Varying Complexity
• Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
• Nonlocal Field Theories and their Gravity Duals
• Complexity as a novel probe of quantum quenches: universal scalings and purifications
• Path-Integral Complexity for Perturbed CFTs
• Subsystem Complexity and Holography
• Warped Conformal Field Theory as Lower Spin Gravity
• Tensor Networks from Kinematic Space
• A boundary stress tensor for higher-derivative gravity in AdS and Lifshitz backgrounds
• Path integral optimization as circuit complexity
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• $p$-adic AdS/CFT
• Entanglement Entropy in Warped Conformal Field Theories
• Near-Horizon Geometry and Warped Conformal Symmetry
• Modifications to Holographic Entanglement Entropy in Warped CFT
• Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops
• Chiral Fermions on the Lattice
• From Path Integrals to Tensor Networks for AdS/CFT
• Geometric actions for three-dimensional gravity
• Schwinger Effect and Entanglement Entropy in Confining Geometries
• An Introduction to Chiral Symmetry on the Lattice
• Quasi-normal modes of warped black holes and warped AdS/CFT correspondence
• Warped Weyl fermion partition functions
• Path Integral Optimization for $T\bar{T}$ Deformation
• Critical Exponents of the Chiral Potts Model from Conformal Field Theory
• Correlation Functions of Warped CFT
• A note on the complex SYK model and warped CFTs
• The connection between holographic entanglement and complexity of purification
• Background-independent charges in Topologically Massive Gravity
• Chiral Liouville Gravity
• Locality and anomalies in warped conformal field theory
• A tensor network quotient takes the vacuum to the thermal state
• Complexity and action for warped AdS black holes
• Generalized Gravitational Entropy for Warped Anti-de Sitter Space
• Geodesic bulk diagrams on the Bruhat-Tits tree
• Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity
• Warped Entanglement Entropy
• Aspects of Warped AdS${}_3$/CFT${}_2$ Correspondence
• Entanglement and chaos in warped conformal field theories
• Fermionic topological quantum states as tensor networks
• Revisiting Conserved Charges in Higher Curvature Gravitational Theories
• Phase Transitions in Warped AdS${}_3$ Gravity
• The renormalization group flow in field theories with quenched disorder
• A defect in holographic interpretations of tensor networks
• Evolutions of entanglement and complexity after a thermal quench in massive gravity theory
• The renormalization group in quantum quenched disorder
• The gravitational dynamics of kinematic space
• Exotic massive 3D gravities from truncation
• Subsystem complexity in warped AdS
• Phase transitions in Bergshoeff-Hohm-Townsend Massive Gravity
• Anomalous Gravitation and its Positivity from Entanglement
• Covariant Poisson's equation in torsional Newton-Cartan gravity

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• Complexity measures from geometric actions on Virasoro and Kac-Moody orbits
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• Modular Hamiltonians in flat holography and (W)AdS/WCFT
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• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
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• Building Tensor Networks for Holographic States
• Entanglement wedge reconstruction and correlation measures in mixed states: modular flows versus quantum recovery channels
• Supersymmetric Warped Conformal Field Theory
• Q-curvature and Path Integral Complexity
• Correlations of mixed systems in confining backgrounds
• Near-Extremal Limits of Warped Black Holes
• On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures
• Emergent geometry and path integral optimization for a Lifshitz action
• Complexity for superconformal primaries from BCH techniques
• Chaos, Phase Transitions and Curvature Invariants of (rotating, warped, massive) BTZ Black Holes
• Encoded information of mixed correlations: the views from one dimension higher
• Critical distance and Crofton form in confining geometries
• Entanglement renormalization for quantum fields with boundaries and defects
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