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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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
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.
The bosonic AdS3/CFT2 duality emerges from the Gross-Neveu model via higher-spin composites and fluctuations in competing spin-0 and spin-1 condensates that define the radial bulk coordinate.
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.
Holographic RG flow on a 2D CFT induces JT gravity with bulk lapse as dilaton and recovers TTbar deformation in the Fefferman-Graham limit.
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.
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.
A holographic QCD model with dilaton-dependent Gauss-Bonnet corrections matches lattice thermodynamics and yields non-monotonic η/s plus a critical endpoint.
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.
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.
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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.