A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
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Lecture Notes on Holographic Renormalization
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abstract
We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, of holographic Ward identities, anomalies and RG equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown-York stress energy tensor of de Sitter spacetime is equal, up to a dimension dependent sign, to the Brown-York stress energy tensor of an associated AdS spacetime.
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representative citing papers
Bulk Q-cocycles determine renormalized and anomaly Q-cocycles on asymptotic boundaries of gauge PDEs, with the anomaly structure reproducing the holographic Weyl anomaly in AdS.
Introduces weight-shifting matrices for de Sitter diagrams, generalized with Kronecker products to arbitrary tree-level graphs, to derive massless wavefunction coefficients from conformally coupled seeds.
In AdS3 gravity with double-trace scalar boundary conditions, zero-frequency boson stars are the true ground state below the instability threshold, and hairy black holes carry higher entropy than BTZ at fixed mass and angular momentum.
Explicit planar AdS multi-NUT spacetimes are built via axionic scalars or quadratic gravity, plus planar Kaluza-Klein monopoles with varying magnetic charges.
Finite Carrollian black-hole thermodynamics arises as a double-scaled low-temperature large-N ensemble in AdS/CFT, with the boundary Brown-York stress tensor reproducing the contracted bulk Hamiltonian and first law.
Bulk-to-boundary correlators for spin-s operators in Poincaré-invariant massless theories are linear superpositions of ISO(2)-fixed tensor structures mapped to non-crossing double-line diagrams that are tensor products of loop diagrams, extrapolating to type Ib multiplets in CCFT generated by Wigner
Recovers Minkowski massless integer-spin solution space as smooth limit of AdS solution space for even dimensions via cosmological-constant expansion of source and vev.
Holographic RG flow on a 2D CFT induces JT gravity with bulk lapse as dilaton and recovers TTbar deformation in the Fefferman-Graham limit.
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
Euclidean AdS wormholes, including new oscillatory 'wineglass' saddles, are classified and their on-shell action competition shows when inflation beats a big crunch.
Holographic RG flow induces gravity by evolving boundary conditions from rigid Dirichlet to mixed Dirichlet-Neumann, generating an Einstein-Hilbert term and evading the Weinberg-Witten theorem.
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
In the diagonal (Cartan) sector of AdS3 gravity, the radial flow of the quasi-local stress tensor satisfies an exact T Tbar-like equation, while the boundary time evolution forms an integrable bi-Hamiltonian hierarchy.
Develops a holographic realization of approximate higher-form symmetries via massive antisymmetric tensor fields and derives dualities between boundary theories from bulk Hodge dualities, including constraints on current-current correlators for self-dual cases.
Field theory models with Robin boundary conditions and modular invariance reproduce zero-winding holographic superconductor results in 2D CFTs and interpret fractional vortices via a Little-Parks toy model.
Constructs bulk scalar field representations in Lorentzian AdS4 from boundary primaries via time-ordered propagators and derives their flat-space limits to plane-wave or Carrollian bases.
Thermal backreaction modifies de Sitter geometry so that late-exiting modes produce a blue-tilted spectrum n_S ~ 2 while the boundary theory matches the 3d Sp(N) model flow.
Semi-holographic systems with perturbative and holographic sectors exhibit prethermal time crystals through dissipationless modes in hydrodynamic channels plus short-wavelength instabilities that produce inhomogeneities over a wide temperature range.
Soft-wall warped geometries yield rapid, mildly supercooled phase transitions whose TeV-scale gravitational wave signals are accessible to space-based interferometers.
Gauss-Bonnet black branes in five-dimensional AdS gravity are unstable when the Gauss-Bonnet coupling falls outside the conformal collider bounds, with unstable modes connected to boundary causality-violating modes by phase rotation of complex boundary momentum.
A holographic QCD model with dilaton-dependent Gauss-Bonnet corrections matches lattice thermodynamics and yields non-monotonic η/s plus a critical endpoint.
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
citing papers explorer
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The Energy-Momentum-News Complex near Future Null Infinity
A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
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Asymptotic boundary structure of Lagrangian gauge theories
Bulk Q-cocycles determine renormalized and anomaly Q-cocycles on asymptotic boundaries of gauge PDEs, with the anomaly structure reproducing the holographic Weyl anomaly in AdS.
-
Cosmological Weight-Shifting Matrices
Introduces weight-shifting matrices for de Sitter diagrams, generalized with Kronecker products to arbitrary tree-level graphs, to derive massless wavefunction coefficients from conformally coupled seeds.
-
When AdS$_3$ Grows Hair: Boson Stars, Black Holes, and Double-Trace Deformations
In AdS3 gravity with double-trace scalar boundary conditions, zero-frequency boson stars are the true ground state below the instability threshold, and hairy black holes carry higher entropy than BTZ at fixed mass and angular momentum.
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Planar AdS multi-NUT spacetimes and Kaluza-Klein multi-monopoles
Explicit planar AdS multi-NUT spacetimes are built via axionic scalars or quadratic gravity, plus planar Kaluza-Klein monopoles with varying magnetic charges.
-
Large-$N$ Carrollian Thermodynamics from AdS Black-Hole Phase-Space Contractions
Finite Carrollian black-hole thermodynamics arises as a double-scaled low-temperature large-N ensemble in AdS/CFT, with the boundary Brown-York stress tensor reproducing the contracted bulk Hamiltonian and first law.
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Spinning bulk-to-boundary correlators in the massless theories with Poincar\'e symmetry
Bulk-to-boundary correlators for spin-s operators in Poincaré-invariant massless theories are linear superpositions of ISO(2)-fixed tensor structures mapped to non-crossing double-line diagrams that are tensor products of loop diagrams, extrapolating to type Ib multiplets in CCFT generated by Wigner
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Flat from AdS: in any dimension and for any spin
Recovers Minkowski massless integer-spin solution space as smooth limit of AdS solution space for even dimensions via cosmological-constant expansion of source and vev.
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GR from RG, $2d$ Example: JT-Gravity Induced from Renormalization Group Flow
Holographic RG flow on a 2D CFT induces JT gravity with bulk lapse as dilaton and recovers TTbar deformation in the Fefferman-Graham limit.
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Higher-spin composites and emergent AdS$_3$ geometry in the $(1+1)$-dimensional Gross-Neveu model
The paper proposes that condensate competition in the 2d Gross-Neveu model generates an emergent AdS₃ bulk, a higher-spin tower, D1-branes, and linearized Einstein gravity with G₃ = ℓ_AdS/4πN².
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A Menagerie of Wormholes and Cosmologies in the Gravitational Path Integral
Euclidean AdS wormholes, including new oscillatory 'wineglass' saddles, are classified and their on-shell action competition shows when inflation beats a big crunch.
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GR from RG: Gravity Is Induced From Renormalization Group Flow In The Infrared
Holographic RG flow induces gravity by evolving boundary conditions from rigid Dirichlet to mixed Dirichlet-Neumann, generating an Einstein-Hilbert term and evading the Weinberg-Witten theorem.
-
Inner Horizon Saddles and a Spectral KSW Criterion
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
-
On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity
In the diagonal (Cartan) sector of AdS3 gravity, the radial flow of the quasi-local stress tensor satisfies an exact T Tbar-like equation, while the boundary time evolution forms an integrable bi-Hamiltonian hierarchy.
-
Approximate higher-form symmetries and dualities of massive p-forms in the holographic bulk
Develops a holographic realization of approximate higher-form symmetries via massive antisymmetric tensor fields and derives dualities between boundary theories from bulk Hodge dualities, including constraints on current-current correlators for self-dual cases.
-
Field Theory Models for a Holographic Superconductor in Two Dimensions
Field theory models with Robin boundary conditions and modular invariance reproduce zero-winding holographic superconductor results in 2D CFTs and interpret fractional vortices via a Little-Parks toy model.
-
On bulk reconstruction in Lorentzian AdS and its flat space limit
Constructs bulk scalar field representations in Lorentzian AdS4 from boundary primaries via time-ordered propagators and derives their flat-space limits to plane-wave or Carrollian bases.
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The thermal backreaction of a scalar field in de Sitter spacetime. II. Spectrum enhancement and holography
Thermal backreaction modifies de Sitter geometry so that late-exiting modes produce a blue-tilted spectrum n_S ~ 2 while the boundary theory matches the 3d Sp(N) model flow.
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On prethermal time crystals from semi-holography
Semi-holographic systems with perturbative and holographic sectors exhibit prethermal time crystals through dissipationless modes in hydrodynamic channels plus short-wavelength instabilities that produce inhomogeneities over a wide temperature range.
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Uncool soft-wall transitions and gravitational waves
Soft-wall warped geometries yield rapid, mildly supercooled phase transitions whose TeV-scale gravitational wave signals are accessible to space-based interferometers.
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Instability of 5D Gauss-Bonnet black branes
Gauss-Bonnet black branes in five-dimensional AdS gravity are unstable when the Gauss-Bonnet coupling falls outside the conformal collider bounds, with unstable modes connected to boundary causality-violating modes by phase rotation of complex boundary momentum.
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Thermodynamics and transport in holographic QCD with Gauss-Bonnet corrections
A holographic QCD model with dilaton-dependent Gauss-Bonnet corrections matches lattice thermodynamics and yields non-monotonic η/s plus a critical endpoint.
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Rethinking quantum information in gravity and fields
The paper organizes important open questions in quantum gravity and quantum information into four themes without presenting new results or derivations.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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Quantum chaos and the holographic principle
A review of the chaos-assisted holographic correspondence linking the SYK model to 2D JT gravity, including the need for string theory corrections at fine quantum scales.
- Bound states and deconfinement from Romans supergravity with magnetic flux