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.

53 pages, v3: matches version published in Nuclear Physics B

References in corpus (15)

• Quantum Gravity at a Lifshitz Point
• Gravity duals for non-relativistic CFTs
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Three-Dimensional Gravity Revisited
• Warped AdS_3 Black Holes
• Non-relativistic holography
• Newtonian Gravity and the Bargmann Algebra
• Dynamics of Carroll Particles
• Lifshitz Space-Times for Schroedinger Holography
• Central Charge for AdS_2 Quantum Gravity
• Two Virasoro symmetries in stringy warped AdS${}_3$
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Holographic Chern-Simons Theories
• Hall viscosity, spin density, and torsion
• Hydrodynamics on the lowest Landau level

Cited by in corpus (15)

• AdS Carroll Chern-Simons supergravity in 2+1 dimensions and its flat limit
• Torsional Newton-Cartan Geometry from the Noether Procedure
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Phase Transitions in Warped AdS${}_3$ Gravity
• N-extended Chern-Simons Carrollian supergravities in 2+1 spacetime dimensions
• Complexity and Emergence of Warped ${\text{AdS}}_3$ Space-time from Chiral Liouville Action
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Supersymmetric Warped Conformal Field Theory
• Conserved charges in timelike Warped-AdS${}_3$ spaces
• Comments on AdS_2 Gravity
• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Holographic entropy of Warped-AdS${}_3$ black holes
• Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant
• Boundary Conditions for Warped AdS${}_3$ in Quadratic Ensemble
• Developments in non-relativistic field theory and complexity