Warped Conformal Field Theory as Lower Spin Gravity

Abstract

Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL(2,R) x U(1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non AdS geometries. This case represents the first step towards understanding a fully invariant formalism for W_N field theories and their holographic duals.

arXiv comment53 pages, v3: matches version published in Nuclear Physics B

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• Holographic Reconstruction of 3D Flat Space-Time
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• Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
• Modifications to Holographic Entanglement Entropy in Warped CFT
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• Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum
• Non-relativistic and Carrollian limits of Jackiw-Teitelboim gravity
• Warped Weyl fermion partition functions
• Correlation Functions of Warped CFT
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• Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension
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• Torsional Newton-Cartan Geometry from the Noether Procedure
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• Near horizon dynamics of three dimensional black holes
• Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms
• Warped Symmetries of the Kerr Black Hole
• The Symmetries of the Carroll Superparticle
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Entanglement and chaos in warped conformal field theories
• Volume and complexity for warped AdS black holes
• Phase Transitions in Warped AdS${}_3$ Gravity
• Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity
• Warped Black Holes in Lower-Spin Gravity
• Non-Riemannian gravity actions from double field theory
• Charged Quantum Fields in AdS${}_2$
• A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities
• Homogeneous Nonrelativistic Geometries as Coset Spaces
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• A BMS-invariant free fermion model
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• Matrix Theory Reloaded: A BPS Road to Holography
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• Complexity of warped conformal field theory
• Complexity and Emergence of Warped ${\text{AdS}}_3$ Space-time from Chiral Liouville Action
• Reflected Entropy in AdS${}_3$/WCFT
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• Subsystem complexity in warped AdS
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
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• Structure Constants from Modularity in Warped CFT
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• Supersymmetric Warped Conformal Field Theory
• Rényi Mutual Information in Holographic Warped CFTs
• Near-Extremal Limits of Warped CFTs
• Conserved charges in timelike Warped-AdS${}_3$ spaces
• Phase transitions in Bergshoeff-Hohm-Townsend Massive Gravity
• Extremal Higher Spin Black Holes
• New Chiral Gravity
• Carroll membranes
• Near-Extremal Limits of Warped Black Holes
• Extended Kinematical 3D Gravity Theories
• Universal features of Lifshitz Green's functions from holography
• Torsion and anomalies in the warped limit of Lifschitz theories
• Systematics of Boundary Actions in Gauge Theory and Gravity
• Comments on AdS_2 Gravity
• Irrelevant and marginal deformed BMS field theories
• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Holographic Entanglement Entropy in NMG
• Warped Flatland
• Note on Bulk Reconstruction in AdS${}_3$/WCFT${}_2$
• Holographic entanglement entropy and modular Hamiltonian in warped CFT in the framework of GMMG model
• A Selberg zeta function for warped AdS${}_3$ black holes
• Warped Conformal Symmetries of the Accelerating Kerr Black Hole
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• Anisotropic conformal Carroll field theories and their gravity duals
• Holographic entropy of Warped-AdS${}_3$ black holes
• Critical points of WAdS/CFT and higher-curvature gravity
• Conserved charges and asymptotic symmetries of BTZ-like black holes in Einstein-bumblebee gravity
• Warped CFT duals of the Plebański-Demiański family of solutions
• Boundary Conditions for Warped AdS${}_3$ in Quadratic Ensemble
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• Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant
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• AdS_3: the NHEK generation