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Large N Field Theories, String Theory and Gravity
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Large N Field Theories, String Theory and Gravity
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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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Cited by 60 Pith papers
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On the strong coupling limit of Yang-Mills matrix models
In mass-deformed Yang–Mills matrix models, strong-coupling commutativity sets in at or above the critical fermion count N_c = 2(D−2), with the supersymmetric models sitting at the critical boundary where huge-operator...
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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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After the Fluid: Subexponential Decay in AdS$_4$
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.
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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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Chaos of Berry curvature for BPS microstates
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.
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The OPE Approach to Renormalization: Operator Mixing
OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
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Hofstadter's Butterfly in AdS$_3$ Black Holes
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.
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The 2-Dimensional Dual of $\phi^4$ in AdS$_3$
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-t...
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Causality constraints and anisotropic states
In anisotropic relativistic fluids, branch-point dispersion relations force a continuum of complex-wavevector mode collisions, and causality bounds the convergence radius direction-by-direction in terms of transport c...
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2-loop free energy of M2 brane in AdS$_7 \times$ S$^4$ and surface defect anomaly in (2,0) theory
The 2-loop (1/N) correction to the M2-brane free energy in AdS7×S4 vanishes in dimensional and ζ-function regularizations, so the boundary defect anomaly is b = 12N − 9, supporting the U(N) (2,0) interpretation.
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Statistics of correlations in nonlinear recurrent neural networks
A replica path-integral calculation yields analytic large-N formulas for covariance statistics and participation dimension in nonlinear recurrent neural networks with quenched Gaussian disorder, confirmed by simulation.
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Living on the edge: a non-perturbative resolution to the negativity of bulk entropies
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.
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Holographic timelike complexity for de Sitter
Timelike subregion volume complexity in de Sitter grows exponentially early and diverges hyperfast at a maximal duration; near the SdS black hole horizon the divergence is replaced by slower, claimed-nonlinear growth.
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Page transition for the complexity of an evaporating black hole
The complexity of radiation from an evaporating black hole is argued to undergo a sharp Page-like transition, dominated after the Page time by the volume of an island in the entanglement wedge.
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The black hole S-matrix in gauge/gravity duality
A unitary black hole S-matrix is built in AdS/CFT via collapsing brane shells; the black hole decays by exponentially rare brane emission, and the emitted branes are argued to be the original constituents, resolving t...
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Analytic HTEE in Moving Plasmas and Its Transition
Analytic holographic timelike entanglement entropy for a boosted BTZ black hole, with a critical boost separating complex and real extremal-geodesic branches.
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Neumann scalars in AdS: partition functions and phases
Neumann scalars in AdS admit one-loop partition functions obtained by contour deformation from the Dirichlet result; the stricter unitarity bound then yields qualitatively different phase diagrams that are corroborate...
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Deformed BTZ Radiance and Single Trace $T\bar{T}$ Holography
Long-string emission from rotating λ-deformed BTZ black holes forces a unique origin B-field that matches the value needed for the string spectrum to agree with the Z_w sector of single-trace T T-bar deformed orbifold...
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Off-shell Hessian thermodynamic stability of higher-curvature black holes
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.
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Emergent $\text{AdS}_{d+1}$ Geometry from Functional Renormalization Group via Bulk Metric Reconstruction
Functional renormalization group applied to the O(N) vector model generates an emergent regular AdS_{d+1} geometry whose near-horizon thermodynamics reproduces the first law and Bekenstein-Hawking area law with temper...
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Strong-coupling results in (non-)conformal $\mathcal{N}=2$ theories with fundamental flavors
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.
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Bound states and deconfinement from Romans supergravity with magnetic flux
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 ...
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Confinement in a finite duality cascade
Holographic checks confirm area-law confinement, anomaly-matching domain walls via 2+1D TQFT, and unstable axionic strings implying no massless axions in this finite duality cascade model.
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Wilson loop in AdS$_3 \times S^3 \times T^4$ from quantum M2 brane
The 1-loop M2-brane correction to the AdS2 imes S1 Wilson-loop partition function in AdS3 imes S3 imes T5 is exactly κ/√(2π) with no subleading 1/κ series.
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Wilson loop in AdS$_3 \times S^3 \times T^4$ from quantum M2 brane
The 1-loop M2-brane partition function for the Wilson loop in AdS3 x S3 x T4 equals kappa over sqrt(2 pi) with no higher-genus string corrections.
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Continuous symmetries and charge measurement of boundary operators in holography
Continuous symmetry operators in holography are U-shaped hanging brane bound states (D5-KK in Type IIB, M5-KK in M-theory) whose worldvolume couplings reproduce the Gauss-law symmetry operators and measure charges of ...
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Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel
Reorganizing the transseries of matrix Bessel kernel determinants at strong coupling yields a simple structure where non-perturbative corrections are directly determined by the perturbative series for N=4 SYM observables.
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Strong coupling structure of $\mathcal{N}=4$ SYM observables with matrix Bessel kernel
The strong-coupling transseries for matrix Bessel determinant observables is generated from its perturbative part by shifting a→a−Δ and replacing moments I_n, with all Stokes constants fixed by two recurrences.
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Light dilaton from top-down holographic confinement with magnetic fluxes
In a two-flux family of top-down holographic confining theories, the lightest scalar is an approximate dilaton with mass about one tenth of the lightest spin-2 confinement scale, over a wide, untuned region of paramet...
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Holographic Equidistribution
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.
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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.
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A Reverse Black Hole Information Problem
Exact CFT states for colliding particles that form evaporating AdS black holes are constructed, and several coarse-graining maps are shown to convert the exact pure state into mixed semiclassical Hawking radiation wit...
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Correspondence between quasinormal modes and grey-body factors of Schwarzschild--Tangherlini black holes
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...
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Soft Algebras in AdS$_4$ from Light Ray Operators in CFT$_3$
A conformal map identifies the flat-space soft gluon S-algebra with light-ray operators built from CFT3 currents and their descendants in AdS4.
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Non-supersymmetric strings on AdS$_3$: a world-sheet perspective
On AdS3×S3×S3×S1, a Wilson-line deformation of the Spin(16)×Spin(16)⋊Z2 heterotic string produces a level-matched tachyon, so the classical moduli space contains unstable regions.
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Loop Corrected Supercharges from Holomorphic Anomalies
The complete one-loop supercharge for 4d Lagrangian SUSY gauge theories is derived in the holomorphic twist, packaged for N=4 SYM as a compact superfield formula.
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Geometry Induced Chiral Transport and Entanglement in $AdS_2$ Background
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.
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Entanglement inequalities, black holes and the architecture of typical states
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 ...
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Toward Krylov-based holography in double-scaled SYK
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-ge...
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Statistics of correlations in nonlinear recurrent neural networks
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.
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Holographic Aspects of Dynamical Mean-Field Theory
DMFT on a Bethe lattice is rewritten as a holographic RG whose fixed point is the DMFT self-consistent solution, and boundary correlation exponents Δ_G, Δ_D track the Mott transition at finite branching number.
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New phases in QCD at finite temperature and chemical potential
In the Veneziano large-N_c limit, QCD at finite baryon chemical potential has two partially deconfined phases (PD-1, PD-2) and two confined phases (CC-1, CC-2), separated by a Gross-Witten-Wadia transition that can be...
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Engineering of Anyons on M5-Probes via Flux Quantization
Flux quantization of the M5-brane tensor field in twisted Cohomotopy yields Pontrjagin homology observables that reproduce abelian Chern-Simons theory and braid actions on defect anyons.
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Carrollian Perspective on Celestial Holography
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.
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One-point holographic correlator in the expanding universe
In the RS-II braneworld with p-brane gas, the holographic thermal one-point function of heavy operators inherits its time dependence from the brane motion: late-time power-law decays τ^{-Δ/2}, τ^{-2Δ/3}, τ^{-Δ} for ra...
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New insights on mutual information in the island approach to the Page curve
At scrambling time I(B+:B−)=0 forces I(I:R)→∞, interpreted as conservation of geometric correlation, while I(I:R+:R−) is shown always negative via Cauchy-slice identities.
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Neumann scalars in AdS: partition functions and phases
Neumann-boundary scalars in AdS_{2..5} get one-loop phase diagrams that are much more restricted than the Dirichlet ones, and symmetry breaking is often blocked by unitarity and thermal-series convergence constraints.
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Singularities, Entropy and the Arrow of Time, {\it or} Is CRT a Gauge Symmetry in Quantum Gravity?
CRT is an asymptotic gauge symmetry in flat/AdS quantum gravity, not a true gauge symmetry, and is absent or only spontaneously broken under special untestable conditions in de Sitter cosmologies.
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Deformed BTZ Radiance and Single Trace $T\bar{T}$ Holography
Generalizes holar wind to lambda-deformed rotating BTZ, finds emission rates set by Delta S_BH and fixes background B-field at origin to match Z_w twisted sector of single-trace TTbar orbifold.
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Holographic Entanglement Anisotropy as a Dark Deformation RG Probe in Hyperscaling-Violating $p$-Wave Superfluids
Strip entanglement anisotropy S⊥−S∥ classifies dark portals in HSV p-wave superfluids into rigid rescalings versus width-running kinetic deformations with short-width W² decoupling.
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Hydrodynamics of Nonminimal $F^{(a)\alpha \beta } F^{(a)\gamma \lambda } R_{\alpha \gamma } R_{\beta \lambda }$ AdS Black Brane
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.
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Emergent $\text{AdS}_{d+1}$ Geometry from Functional Renormalization Group via Bulk Metric Reconstruction
Functional renormalization group flow of the O(N) vector model produces an emergent AdS_{d+1} geometry under the massless critical condition.
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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 Thermodynamics of Cosmological Horizons and Their Holographic Description in de Sitter Space
A universal first law of thermodynamics for de Sitter cosmological horizons defines entropy in the holographic dual at future infinity as a function of boundary pressure and angular momentum from the Brown-York stress tensor.
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Low-energy hadronic physics in holographic $\mathrm{QCD_{3}}$ with anisotropy
In an anisotropic holographic model of 3D QCD, hadronic systems become unstable when anisotropy exceeds the confinement energy scale, with dragging terms essential for transport properties.
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Confinement in a finite duality cascade
Holographic consistency checks confirm confinement (area law), domain-wall dynamics matching YM-CS theory, and absence of stable axionic strings in a D3/O7-conifold gauge/gravity dual.
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Instability in ${\cal N}=4$ supersymmetric Yang-Mills theory on $S^3$ at finite density
On S^3, curvature can stabilize R-symmetry charge transport of charged N=4 SYM plasma while thermodynamic instability persists, and volume fluctuations never restore thermodynamic stability.
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Instability in ${\cal N}=4$ supersymmetric Yang-Mills theory on $S^3$ at finite density
Curvature on S^3 decouples dynamical instabilities in R-charge transport from thermodynamic instabilities in N=4 SYM plasma at finite density, with thermodynamic instability persisting under volume fluctuations.
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Heavy Quarkonium Spectrum and Decay Constants from a Neural-Network-Based Holographic Model
A neural-network-parametrized dilaton field reproduces the masses and leptonic decay constants of charmonium and bottomonium with 1.26% and 3.32% RMS errors, but only because those values were used as training data.
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Probing phase transitions of regular black holes in anti-de Sitter space with Lyapunov exponent
For charged regular AdS black holes in quasi-topological gravity, the null-geodesic Lyapunov exponent jumps at the first-order phase transition and its phase difference vanishes at the critical point with exponent 1/2...
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