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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Large N Field Theories, String Theory and Gravity
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abstract
We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.
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Real-analytic perturbations of AdS4 black branes exhibit stretched-exponential decay exp(-c t^{5/6}) controlled by the large-k tail of the quasinormal mode spectrum.
The one-loop diagram in conformally coupled φ⁴ theory in AdS₃ is expressed as an infinite sum of tree-level diagrams, summed via number-theoretic conjectures to give analytic anomalous dimensions for all dual double-trace operators, with new results in t- and u-channels.
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
Berry curvature of BPS states is random-matrix-like for supersymmetric black hole microstates but non-random and often zero for horizonless geometries, offering a chaos diagnostic in degenerate sectors.
OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
A single-band lattice model on the BTZ cylinder produces a curvature-dependent Harper equation whose spectra show sharpened butterfly fragmentation at weak curvature and suppressed magnetic response near larger horizons.
An off-shell Hessian criterion H = S'_W(r_h) T'(r_h) governs thermodynamic stability of higher-curvature black holes, recovering the temperature-slope rule on physical branches and producing mean-field critical exponents.
Localization matrix models yield resummed strong-coupling expressions for observables in N=2 theories with antisymmetric and fundamental matter, using an effective 't Hooft coupling at large N.
Holographic analysis of Romans supergravity solutions with Abelian magnetic flux yields a family of confining 4D duals featuring a flux-driven first-order deconfinement transition and two parametrically light, nearly degenerate scalar bound states near the transition.
Equidistribution of Hecke operators in large N CFT limits reduces the partition function to light-state Poincaré series with an immediate interpretation as sums over handlebody geometries.
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.
Quasinormal modes correspond well to grey-body factors for vector and tensor perturbations of Schwarzschild-Tangherlini black holes in all dimensions, but fail for scalar l=2 modes in D≥7 because of multiple potential barriers.
A conformal map identifies the flat-space soft gluon S-algebra with light-ray operators built from CFT3 currents and their descendants in AdS4.
Curvature in AdS2 generates effective fields causing asymmetric chiral fermion propagation confined in Lieb-Robinson cones, with entanglement entropy growing then saturating and peaking in dipole collisions.
Typical states in large-N holographic CFTs exhibit UV and IR length scales set by energy and charges, producing factorization that isolates black holes via a corona of saturated entanglement wedges and extends ETH to rotating ensembles.
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-geometry von Neumann entropy after tracing baby universes.
Derives exact correlation statistics for nonlinear RNNs in the large-N limit with Gaussian quenched disorder using path integrals, generalizing linear results and adding 1/N corrections.
A 3d sourced conformal Carrollian field theory is proposed to holographically capture 4d flat gravity kinematics, with Ward identities matching 2d celestial CFT after relating operators.
Perturbative holographic calculation yields σ = 1 − q₂(9κQ²/(L² r_h⁴) + 7κ²Q⁴/(4 r_h⁸)) and η/s = (1/(4π))(1 + q₂ 7κ²Q⁴/(2 r_h⁸)) for a nonminimal AdS black brane.
Functional renormalization group flow of the O(N) vector model produces an emergent AdS_{d+1} geometry under the massless critical condition.
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.
Density-of-states lattice study of the first-order phase transition in Sp(4) Yang-Mills theory at finite temperature, confirming metastability and surface tension for two temporal extents toward the continuum limit.
Derives perturbative 4D nonminimal Maxwell-AdS black hole and reports Van der Waals-like behavior plus Hawking-Page transitions in its thermodynamics.
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Lectures on Naturalness, String Landscape and Multiverse
Lecture notes providing a technical introduction to naturalness problems and the string theory landscape for graduate students.