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Lecture Notes on Holographic Renormalization
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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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Showing 60 of 66 Pith papers that cite this
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Non-Hermitian Holographic Flows to Little Rip Cosmologies
A holographic model of a non-Hermitian PT-symmetric QFT produces black hole interiors that are isotropic Little Rip cosmologies, separated from standard Kasner behavior by a distinctive logarithmic signature in heavy-...
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Localised Horizons and Holographic Thermodynamics: Supercooling in the 1/D Expansion
For a large class of holographic confining gauge theories far from conformality, the maximum supercooling equals half the squared speed of sound at the critical temperature, up to 1/D corrections.
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Holographic Learning from Fermionic Spectra: Application to Strange Metal Phenomenology
Neural ODEs learn that normalized low-T cuprate PLL spectra are well described by conformal-to-AdS2 black holes with nearly vanishing gauge potential, while thermodynamics remain invisible to the massless probe.
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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.
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4d CFT Correlators from Ambitwistors
Conserved spinning two- and three-point correlators in 4d CFTs are obtained from holomorphic contour integrals on ambitwistor space, with spin, parity, and even a conformally coupled scalar treated uniformly.
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Cosmological Weight-Shifting Matrices
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Bound states and deconfinement from Romans supergravity with magnetic flux
Holographic duals from Romans supergravity with Abelian magnetic flux yield confining 4D theories with a flux-driven zero-temperature deconfinement transition and a spectrum dominated by two nearly degenerate light sc...
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Flat Holography & Holographic Renormalization: Scalar Field
A Hamilton-Jacobi holographic renormalization scheme for scalars in Minkowski space yields a GKPW-style flat holography dictionary: source = scattering data, vev = renormalized momentum, with correlators matching the ...
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The Effects of Near-AdS$_2$ Backreaction on Matter Fields
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Symmetry TFTs for Continuous Spacetime Symmetries
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Linearized gravity in a cavity with conformal boundary conditions is ill-posed: a sequence of smooth perturbations with vanishing initial data grows without bound at every positive time.
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Entanglement Entropy of a Scalar Field in Anti-de Sitter Space
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Tantum Gravity
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Exact low-temperature Green's functions in AdS/CFT: From Heun to confluent Heun
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Source and Response Soft Charges for Maxwell Theory on $AdS_d$
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Little String Theories on Curved Manifolds
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Flavour current correlators and the non-Abelian hydrodynamic approximation: the charged sector
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On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity
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Large-$N$ Carrollian Thermodynamics from AdS Black-Hole Phase-Space Contractions
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Spinning bulk-to-boundary correlators in the massless theories with Poincar\'e symmetry
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GR from RG, $2d$ Example: JT-Gravity Induced from Renormalization Group Flow
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A Menagerie of Wormholes and Cosmologies in the Gravitational Path Integral
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GR from RG: Gravity Is Induced From Renormalization Group Flow In The Infrared
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$SO(1, d + 1)$ symmetry of the Exact RG equation
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Holographic Turbulence and Numerical Estimate of the Fractal Dimension of the Turbulent Horizon
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Quantum chaos and pole skipping in two-dimensional conformal perturbation theory
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Finite-cutoff Holographic Thermodynamics
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Ensembles in M-theory and Holography
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Gravitational Observatories in AdS$_4$
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Derivation of the GKP-Witten relation by symmetry without Lagrangian
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Generalized Fefferman-Graham gauge and boundary Weyl structures
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The QNEC gives a universal upper bound on the quadratic growth rate of quench entanglement entropy, and this bound is saturated by boundary state quenches.
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Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
Kounterterm renormalization is extended to even-dimensional holographic CFTs, yielding a universal entanglement entropy formula whose logarithmic coefficient reproduces the type A central charge.
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Entanglement entropy and $T\bar T$ deformations beyond antipodal points from holography
For a holographic (A)dS spacetime with a hard radial cutoff, the entanglement entropy of any interval on the sphere equals the antipodal-point formula with radius R cos(beta_epsilon).
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Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit
For JT gravity with conformal matter, the generalized entropy defined from the horizon dilaton plus matter entanglement is monotonic along the event horizon and along future Q-screens under the null energy condition, ...
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Type IIB Supergravity Action and Holography
A milder topological correction to the PST Type IIB action yields non-vanishing on-shell values matching holography for Lunin-Maldacena and AdS4 S-fold backgrounds.
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Field Theory Models for a Holographic Superconductor in Two Dimensions
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On bulk reconstruction in Lorentzian AdS and its flat space limit
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Renormalized pseudoentropy in dS/CFT
Renormalized holographic pseudoentropy in dS/CFT is constructed from conformal-gravity actions in four and six dimensions, yielding finite sphere values and Mezei-like shape dependence for small deformations.
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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 inhomogeneiti...
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Chiral phase transition: effective field theory and holography
A Schwinger-Keldysh effective field theory for the chiral phase transition, with chiral charges and condensate as dynamical variables, is constructed and its coefficients are computed in a modified AdS/QCD model, with...
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On the stability of holographic confinement with magnetic fluxes
A bottom-up holographic model with magnetic flux on a circle shows a confining-to-conformal phase transition that occurs before a tachyonic instability, with the lightest scalar near the transition resembling a dilaton.
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Thermodynamic Topology of 4D Charged AdS Black Holes with $F^{\alpha\beta}F^{\gamma\lambda}R_{\alpha\gamma\beta\lambda}$ Coupling
A 4D charged AdS black hole with an FFR non-minimal coupling has van der Waals criticality and belongs to topological class W_{1+} with winding numbers (+1, -1, +1).
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Dilatonic states, phase transitions, and criticality in holography
A review of holographic examples indicating that a light dilaton appears near critical endpoints of first-order zero-temperature phase transitions, with explicit but lower-dimensional demonstrations.
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