Aspects of the zero $\Lambda$ limit in the AdS/CFT correspondence

Abstract

We examine the correspondence between QFT observables and bulk solutions in the context of AdS/CFT in the limit as the cosmological constant $\Lambda \to 0$. We focus specifically on the spacetime metric and a non-backreacting scalar in the bulk, compute the one-point functions of the dual operators and determine the necessary conditions for the correspondence to admit a well-behaved zero $\Lambda$ limit. We discuss holographic renormalization in this limit and find that it requires schemes that partially break diffeomorphism invariance of the bulk theory. In the specific case of three bulk dimensions, we compute the zero $\Lambda$ limit of the holographic Weyl anomaly and reproduce the central charge that arises in the central extension of ${\mathfrak{bms}}_3$. We compute holographically the energy and momentum of those QFT states dual to flat cosmological solutions and to the Kerr solution and find an agreement with the bulk theory. We also compute holographically the renormalized 2-point function of a scalar operator in the zero $\Lambda$ limit and find it to be consistent with that of a conformal operator in two dimensions less. Finally, our results can be used in a new definition of asymptotic Ricci-flatness at null infinity based on the zero $\Lambda$ limit of asymptotically Einstein manifolds.

70 pages. v3: published version

References in corpus (14)

• Quantum Gravity at a Lifshitz Point
• The BMS/GCA correspondence
• Holography of 3d Flat Cosmological Horizons
• Entropy of three-dimensional asymptotically flat cosmological solutions
• Local bulk S-matrix elements and CFT singularities
• A classification of near-horizon geometries of extremal vacuum black holes
• Holographic renormalization as a canonical transformation
• String scattering in flat space and a scaling limit of Yang-Mills correlators
• Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes
• Scale invariance vs conformal invariance
• On the Stress Tensor for Asymptotically Flat Gravity
• Asymptotic flatness at null infinity in higher dimensional gravity
• Higher Dimensional Bondi Energy with a Globally Specified Background Structure
• Holographic Renormalization of Asymptotically Flat Gravity

Cited by in corpus (20)

• Entanglement entropy in Galilean conformal field theories and flat holography
• BMS Particles in Three Dimensions
• Stress tensor correlators in three-dimensional gravity
• 3D Flat Holography: Entropy and Logarithmic Corrections
• Variational principle and 1-point functions in 3-dimensional flat space Einstein gravity
• Wilson Lines and Holographic Entanglement Entropy in Galilean Conformal Field Theories
• Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra
• General null asymptotics and superrotation-compatible configuration spaces in $d\ge 4$
• Aspects of Flat/CCFT Correspondence
• N=4 Supersymmetric BMS3 algebras from asymptotic symmetry analysis
• Boundary dynamics of asymptotically flat 3D gravity coupled to higher spin fields
• Stress Tensor on Null Boundaries
• Rindler/Contracted-CFT Correspondence
• How General Is Holography?
• Complexity Growth in Flat Spacetimes
• Aspects of Ultra-Relativistic Field Theories via Flat-space Holography
• Black holes and thermodynamics - The first half century
• Stress Tensor Correlators of CCFT${}_2$ using Flat-Space Holography
• Kaluza-Klein reductions and AdS/Ricci-flat correspondence
• Contractions from Grading