Reading Guide to the Literature

Why a reading guide belongs in a computation toolkit

A serious holographer reads papers differently from a tourist. A tourist asks, “What is the result?” A researcher asks:

1. What is the precise boundary observable?
2. What is the bulk variational problem?
3. Which approximation is being used?
4. Which normalizations and boundary conditions control the answer?
5. What survives outside the special model?

The AdS/CFT literature is now too large for a linear bibliography. The right goal is not to read everything. The right goal is to build a working map: original papers for first principles, reviews for efficient orientation, technical papers for calculations, and modern papers for current conceptual structure.

This guide is therefore opinionated. It emphasizes papers that teach durable methods, not merely famous results. When a paper is historically important but difficult on first reading, the guide says what to extract from it rather than pretending every classic is the best pedagogical entry point.

How to use this page

Use the literature in three passes.

First pass: orientation. Read introductions, abstracts, and the first nontrivial formula. Ask what problem the paper solved and which dictionary entry it clarified.

Second pass: reconstruction. Reproduce one calculation from the paper. For a correlator paper, reproduce a two-point function. For a black-hole paper, reproduce temperature and entropy. For an entanglement paper, reproduce the simplest minimal surface.

Third pass: research extraction. Write down the assumptions in a form you can vary. A good research question often begins by changing one assumption while keeping the calculational structure intact.

A useful reading log has the following format.

Item	Question to answer
Observable	What is computed on the CFT side?
Bulk object	Which field, brane, surface, or geometry computes it?
Limit	Exact, large $N$, large $\lambda$, probe, hydrodynamic, semiclassical, or numerical?
Boundary data	Which quantities are sources and which are vevs?
Interior condition	Regularity, infalling condition, smooth Euclidean cap, extremality, or horizon boundary condition?
Renormalization	Which counterterms, contact terms, or scheme choices enter?
Universal part	What is independent of the model?
Fragile part	What depends on supersymmetry, conformality, two-derivative gravity, probe limits, or special dimensions?

The rest of this page is organized by purpose.

The irreducible starting set

These papers are the minimum historical and conceptual foundation.

Topic	Reference	Read for
The conjecture	Maldacena, “The Large $N$ Limit of Superconformal Field Theories and Supergravity”	The brane decoupling logic and the idea that near-horizon geometries define dual quantum theories.
Correlator prescription	Gubser, Klebanov, Polyakov, “Gauge Theory Correlators from Non-Critical String Theory”	The source/operator prescription and the use of boundary values of bulk fields.
Boundary-value formulation	Witten, “Anti de Sitter Space and Holography”	The generating-functional formulation, Euclidean AdS, and CFT correlators from bulk actions.
Thermal AdS/CFT	Witten, “Anti-de Sitter Space, Thermal Phase Transition, and Confinement in Gauge Theories”	Hawking-Page physics, large-$N$ deconfinement, and the Euclidean-saddle viewpoint.
Wilson loops	Maldacena, “Wilson Loops in Large $N$ Field Theories” and Rey-Yee, “Macroscopic Strings as Heavy Quarks”	Fundamental strings ending on boundary loops and the strong-coupling heavy-quark potential.
UV/IR relation	Susskind-Witten, “The Holographic Bound in Anti-de Sitter Space”	The radial/scale intuition and the entropy-counting logic.

A student who has read only these papers will know the origin of the correspondence, but not yet how to compute reliably. For computation, the next layer is essential.

Core reviews and lecture notes

These are the references to keep open while doing calculations.

Reference	Best use
Aharony, Gubser, Maldacena, Ooguri, Oz, “Large $N$ Field Theories, String Theory and Gravity”	The classic broad review. Use it for the canonical dictionary, brane examples, tests, and the early conceptual landscape.
D’Hoker and Freedman, “Supersymmetric Gauge Theories and the AdS/CFT Correspondence”	Detailed correlator technology, supergravity modes, and protected quantities in the canonical example.
Skenderis, “Lecture Notes on Holographic Renormalization”	The best gateway to near-boundary expansions, counterterms, Ward identities, and renormalized one-point functions.
Polchinski, “Introduction to Gauge/Gravity Duality”	A clear string-theory-first path through the duality. Good for conceptual consolidation.
McGreevy, “Holographic Duality with a View Toward Many-Body Physics”	Excellent for learning how the dictionary is used in strongly coupled many-body systems.
Rangamani, “Gravity and Hydrodynamics: Lectures on the Fluid-Gravity Correspondence”	Good entry into hydrodynamic effective theory from gravity.
Harlow, “TASI Lectures on the Emergence of Bulk Physics in AdS/CFT”	Modern conceptual structure: large-$N$ factorization, bulk locality, reconstruction, and quantum error correction.

Do not treat reviews as substitutes for original papers. Treat them as maps. The original papers usually reveal which assumptions were actually made.

Geometry, conformal symmetry, and the boundary

Start here if you want to understand the spacetime side of the correspondence rather than merely manipulate formulas.

Reference	Read for
Gibbons, “Anti-de-Sitter spacetime and its uses”	Global AdS, causal structure, universal cover, and the geometry behind many slogans.
Ishibashi and Wald, “Dynamics in Non-Globally Hyperbolic Static Spacetimes”	Why AdS requires boundary conditions and why the timelike boundary is not a decorative detail.
Gao and Wald, “Theorems on gravitational time delay and related issues”	Boundary causality and why bulk matter satisfying energy conditions cannot casually short-circuit the boundary.
de Haro, Skenderis, Solodukhin, “Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence”	Fefferman-Graham expansions, holographic stress tensors, and recursive near-boundary reconstruction.

The most common beginner mistake is to identify a particular coordinate system with AdS itself. The literature is full of Poincaré coordinates, global coordinates, Fefferman-Graham gauge, Eddington-Finkelstein coordinates, and Kruskal coordinates. They answer different questions.

The canonical $\mathcal N=4$ example and string-theory origins

The canonical duality is not just a slogan; it is a chain of parameter identifications.

Reference	Read for
Polchinski, “Dirichlet-Branes and Ramond-Ramond Charges”	D-branes as dynamical RR-charged objects and the conceptual bridge between open strings and geometry.
Maldacena, “The Large $N$ Limit…”	The two low-energy limits of the D3-brane system.
Itzhaki, Maldacena, Sonnenschein, Yankielowicz, “Supergravity and the Large $N$ Limit of Theories with Sixteen Supercharges”	D$p$-brane validity regimes and the nonconformal generalization of the decoupling logic.
Klebanov, “TASI Lectures: Introduction to the AdS/CFT Correspondence”	A useful early pedagogical account of the D3-brane example and related tests.
Kovacs, “$\mathcal N=4$ Supersymmetric Yang-Mills Theory and the AdS/SCFT Correspondence”	Field-theory details of $\mathcal N=4$ SYM.

For the canonical dictionary, keep the following hierarchy visible:

$$\frac{L^4}{\alpha'^2}\sim \lambda, \qquad g_s \sim \frac{\lambda}{N}, \qquad \frac{L^3}{G_5}\sim N^2.$$

Large $N$ suppresses bulk loops. Large $\lambda$ suppresses stringy $\alpha'$ corrections. These are distinct limits.

CFT data, correlators, and Witten diagrams

These readings teach how bulk perturbation theory becomes CFT data.

Reference	Read for
Gubser, Klebanov, Polyakov and Witten	The generating-functional prescription.
Freedman, Mathur, Matusis, Rastelli, “Correlation Functions in the CFT$_d$/AdS$_{d+1}$ Correspondence”	Explicit two- and three-point correlator calculations.
D’Hoker, Freedman, Mathur, Matusis, Rastelli, “Graviton Exchange and Complete Four-Point Functions…”	Early exchange Witten diagrams and the complexity of four-point functions.
Penedones, “Writing CFT Correlation Functions as AdS Scattering Amplitudes”	Mellin amplitudes and the connection between AdS correlators and scattering intuition.
Heemskerk, Penedones, Polchinski, Sully, “Holography from Conformal Field Theory”	The CFT-first criterion for local bulk effective field theory.
Fitzpatrick, Kaplan, “AdS Field Theory from Conformal Field Theory”	How bulk perturbation theory emerges from large-$N$ CFT data.

When reading a correlator paper, identify whether the normalization is chosen so that two-point functions are $O(1)$, $O(N^2)$, or canonically normalized in the bulk. Many apparent disagreements in coefficients are just normalization choices wearing a trench coat.

Holographic renormalization

Holographic renormalization is the difference between a formal prescription and a well-defined variational problem.

Reference	Read for
de Haro, Skenderis, Solodukhin	Fefferman-Graham reconstruction and holographic stress tensors.
Skenderis, “Lecture Notes on Holographic Renormalization”	The practical counterterm algorithm.
Bianchi, Freedman, Skenderis, “Holographic Renormalization”	RG flows, scalar one-point functions, and supersymmetric domain walls.
Balasubramanian and Kraus, “A Stress Tensor for Anti-de Sitter Gravity”	Brown-York stress tensor plus counterterms.
Henningson and Skenderis, “The Holographic Weyl Anomaly”	The holographic origin of conformal anomalies.

A good exercise with any holographic-renormalization paper is to separate the near-boundary data into three classes:

1. source data fixed as boundary conditions,
2. local response data determined algebraically by the source,
3. nonlocal response data determined by the interior state.

Only the third class carries dynamical information.

Real-time correlators, black holes, and transport

These readings teach how horizons compute dissipative response.

Reference	Read for
Son and Starinets, “Minkowski-space correlators in AdS/CFT”	Retarded Green functions from infalling boundary conditions.
Herzog and Son, “Schwinger-Keldysh Propagators from AdS/CFT”	Real-time contour structure beyond the simple retarded prescription.
Skenderis and van Rees, “Real-time Gauge/Gravity Duality”	A systematic real-time holographic prescription.
Horowitz and Hubeny, “Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium”	Quasinormal modes as relaxation scales.
Policastro, Son, Starinets, “The Shear Viscosity of Strongly Coupled $\mathcal N=4$ SYM Plasma”	The original $\eta/s=1/(4\pi)$ computation.
Kovtun, Son, Starinets, “Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics”	Universality of $\eta/s$ in two-derivative gravity and the original bound proposal.
Iqbal and Liu, “Universality of the Hydrodynamic Limit in AdS/CFT and the Membrane Paradigm”	Horizon data as low-frequency transport data.
Kovtun, “Lectures on Hydrodynamic Fluctuations in Relativistic Theories”	Field-theory hydrodynamics and Kubo formulas.
Hubeny, Minwalla, Rangamani, “The Fluid/Gravity Correspondence”	Nonlinear hydrodynamics from long-wavelength black-brane perturbations.

For transport, always write down the order of limits. DC conductivity, diffusion, static susceptibility, and optical conductivity often differ by whether $\omega\to0$ or $k\to0$ is taken first.

Wilson loops, branes, defects, and flavor

These references explain nonlocal observables and probe sectors.

Reference	Read for
Maldacena, “Wilson Loops in Large $N$ Field Theories”	Fundamental strings ending on Wilson-loop contours.
Rey and Yee, “Macroscopic Strings as Heavy Quarks…”	Heavy probes and quark-antiquark potentials.
Drukker, Gross, Ooguri, “Wilson Loops and Minimal Surfaces”	Minimal-surface subtleties and supersymmetric loop observables.
Witten, “Baryons and Branes in Anti de Sitter Space”	The wrapped-brane baryon vertex.
Karch and Katz, “Adding Flavor to AdS/CFT”	Flavor branes and the probe limit.
Kruczenski, Mateos, Myers, Winters, “Meson Spectroscopy in AdS/CFT with Flavour”	D7-brane meson spectra as normal modes.
DeWolfe, Freedman, Ooguri, “Holography and Defect Conformal Field Theories”	Defect CFTs from intersecting branes.

The recurring diagnostic is scaling. Fundamental strings are $O(\sqrt\lambda)$ in the exponent. Probe flavor sectors are $O(NN_f)$ rather than $O(N^2)$. Wrapped baryon vertices are $O(N)$ objects. If the scaling is wrong, the proposed dictionary entry is probably wrong.

RG flows, confinement, and holographic QCD-like models

Use these references to distinguish top-down flows from bottom-up models.

Reference	Read for
Freedman, Gubser, Pilch, Warner, “Renormalization Group Flows from Holography—Supersymmetry and a $c$-Theorem”	Domain walls, scalar potentials, and holographic $c$-functions.
de Boer, Verlinde, Verlinde, “On the Holographic Renormalization Group”	Hamilton-Jacobi/holographic RG viewpoint.
Gubser, “Curvature Singularities: The Good, the Bad, and the Naked”	Criteria for acceptable singular IR geometries.
Polchinski and Strassler, “Hard Scattering and Gauge/String Duality”	Introducing an IR scale in AdS to model confining dynamics.
Kinar, Schreiber, Sonnenschein, “$Q\bar Q$ Potential from Strings in Curved Spacetime”	Holographic Wilson-loop criteria for confinement.
Erlich, Katz, Son, Stephanov, “QCD and a Holographic Model of Hadrons”	Hard-wall AdS/QCD.
Karch, Katz, Son, Stephanov, “Linear Confinement and AdS/QCD”	Soft-wall AdS/QCD and linear Regge trajectories.
Sakai and Sugimoto, “Low Energy Hadron Physics in Holographic QCD”	Top-down chiral symmetry breaking and mesons/baryons.

A bottom-up holographic model can be valuable without being derived from string theory. The intellectual sin is not using bottom-up models; it is forgetting which conclusions are model-dependent.

Finite density and holographic quantum matter

These readings are the gateway to AdS/CMT.

Reference	Read for
Hartnoll, “Lectures on Holographic Methods for Condensed Matter Physics”	The best first technical guide to finite density, conductivity, and holographic superconductors.
McGreevy, “Holographic Duality with a View Toward Many-Body Physics”	Conceptual orientation for condensed-matter readers.
Gubser, “Breaking an Abelian Gauge Symmetry Near a Black Hole Horizon”	The charged-scalar instability behind holographic superconductors.
Hartnoll, Herzog, Horowitz, “Building a Holographic Superconductor”	The canonical Abelian-Higgs holographic superconductor.
Faulkner, Liu, McGreevy, Vegh, “Emergent Quantum Criticality, Fermi Surfaces, and AdS$_2$”	The AdS$_2$ matching method and finite-density IR physics.
Liu, McGreevy, Vegh, “Non-Fermi Liquids from Holography”	Holographic fermion spectral functions and Fermi surfaces.
Andrade and Withers, “A Simple Holographic Model of Momentum Relaxation”	Linear axions and finite DC conductivity.
Donos and Gauntlett, “Thermoelectric DC Conductivities from Black Hole Horizons”	Horizon formulae for DC transport.

When reading finite-density holography, keep three currents distinct:

$$J^{\mu}, \qquad T^{t\mu}, \qquad J_{\mathrm{inc}}^{\mu}.$$

At nonzero density, electric current overlaps with momentum. Ignoring this is the fastest way to misinterpret DC conductivity.

Entanglement, reconstruction, and quantum error correction

This is the modern conceptual core of holography.

Reference	Read for
Ryu and Takayanagi, “Holographic Derivation of Entanglement Entropy from AdS/CFT”	The RT area formula and the AdS$_3$/CFT$_2$ interval check.
Hubeny, Rangamani, Takayanagi, “A Covariant Holographic Entanglement Entropy Proposal”	The HRT covariant generalization.
Headrick and Takayanagi, “A Holographic Proof of the Strong Subadditivity of Entanglement Entropy”	Geometric entropy inequalities.
Casini, Huerta, Myers, “Towards a Derivation of Holographic Entanglement Entropy”	Ball-region entanglement, hyperbolic black holes, and universal terms.
Lewkowycz and Maldacena, “Generalized Gravitational Entropy”	Replica derivation of RT in classical gravity.
Faulkner, Lewkowycz, Maldacena, “Quantum Corrections to Holographic Entanglement Entropy”	The FLM correction $S_A=\mathrm{Area}/(4G_N)+S_{\mathrm{bulk}}+\cdots$.
Jafferis, Lewkowycz, Maldacena, Suh, “Relative Entropy Equals Bulk Relative Entropy”	JLMS and modular-energy matching.
Almheiri, Dong, Harlow, “Bulk Locality and Quantum Error Correction in AdS/CFT”	The QEC interpretation of bulk locality.
Dong, Harlow, Wall, “Reconstruction of Bulk Operators within the Entanglement Wedge”	Entanglement-wedge reconstruction.
Harlow, “The Ryu-Takayanagi Formula from Quantum Error Correction”	Operator-algebra QEC and the quantum RT formula.

The right way to read this literature is to track which statement lives at which order:

$$O(N^2):\quad \frac{\mathrm{Area}}{4G_N}, \qquad O(N^0):\quad S_{\mathrm{bulk}}, \qquad O(e^{-N^2}):\quad \text{nonperturbative code limitations}.$$

Mixing these orders creates many false paradoxes.

Black-hole information, chaos, and islands

This reading path starts with semiclassical gravity and ends with the modern island rule.

Reference	Read for
Hawking, “Breakdown of Predictability in Gravitational Collapse”	The original pure-to-mixed information-loss argument.
Page, “Information in Black Hole Radiation”	Page-curve logic and typicality.
Maldacena, “Eternal Black Holes in Anti-de Sitter”	The thermofield double and the two-sided AdS black hole.
Almheiri, Marolf, Polchinski, Sully, “Black Holes: Complementarity or Firewalls?”	The firewall sharpening of the paradox.
Harlow, “Jerusalem Lectures on Black Holes and Quantum Information”	A modern information-theoretic entry point.
Shenker and Stanford, “Black Holes and the Butterfly Effect”	Shockwaves and chaos in two-sided black holes.
Maldacena, Shenker, Stanford, “A Bound on Chaos”	The chaos bound $\lambda_L\le 2\pi/\beta$.
Penington, “Entanglement Wedge Reconstruction and the Information Paradox”	Page transition from quantum extremal surfaces.
Almheiri, Engelhardt, Marolf, Maxfield, “The Entropy of Bulk Quantum Fields and the Entanglement Wedge of an Evaporating Black Hole”	Quantum extremal surfaces for evaporating black holes.
Almheiri, Mahajan, Maldacena, Zhao, “The Page Curve of Hawking Radiation from Semiclassical Geometry”	Islands in semiclassical gravitational entropy.
Penington, Shenker, Stanford, Yang, “Replica Wormholes and the Black Hole Interior”	Replica-wormhole derivation of island saddles.
Almheiri, Hartman, Maldacena, Shaghoulian, Tajdini, “Replica Wormholes and the Entropy of Hawking Radiation”	Replica-wormhole derivation from another angle.

A healthy reading habit: never say “islands solve the information paradox” without specifying what is solved. Islands explain the Page curve in semiclassical entropy calculations. They do not by themselves provide a microscopic decoding algorithm, a complete theory of cosmological holography, or a universal treatment of all singularities.

Beyond AdS$_5$/CFT$_4$

The canonical example is central, but AdS/CFT is a family of dualities.

Topic	References	Read for
AdS$_3$/CFT$_2$	Brown-Henneaux, BTZ, Strominger on BTZ entropy	Virasoro symmetry, central charge, BTZ black holes, Cardy entropy.
M2/ABJM	Aharony, Bergman, Jafferis, Maldacena, Drukker, Marino, Putrov	AdS$_4$/CFT$_3$, Chern-Simons matter, $N^{3/2}$ free energy.
M5/6d CFTs	Maldacena, Henningson-Skenderis, Gaiotto	AdS$_7$/CFT$_6$, $N^3$ scaling, compactifications, class-$\mathcal S$ ideas.
Higher spin/vector models	Klebanov-Polyakov, Giombi-Yin, Maldacena-Zhiboedov	Large-$N$ vector models, higher-spin symmetry, and why not all large-$N$ theories have Einstein gravity duals.
Nonconformal branes	Itzhaki et al., Kanitscheider-Skenderis-Taylor	Generalized conformal structure and D$p$-brane holography.
Flat-space holography	Penedones flat-space limit, Strominger lectures, Pasterski-Shao celestial amplitudes	$S$-matrix limits, BMS symmetry, celestial amplitudes.
de Sitter	Strominger dS/CFT, Anninos lectures	Wavefunction observables, cosmological boundaries, and open conceptual problems.

The main lesson of this section is comparative. AdS has a clean timelike boundary and ordinary Hamiltonian evolution in the dual CFT. Flat space and de Sitter do not simply inherit that structure.

Numerical holography and practical computation

Numerical holography is not a separate subject; it is holography when the bulk equations stop being analytically soluble.

Reference	Read for
Headrick, Kitchen, Wiseman, “A New Approach to Static Numerical Relativity…”	The Einstein-DeTurck method and elliptic boundary value problems.
Wiseman, “Numerical Construction of Static and Stationary Black Holes”	Practical numerical black-hole construction.
Dias, Santos, Way, “Numerical Methods for Finding Stationary Gravitational Solutions”	A detailed review of stationary gravitational boundary value problems.
Chesler and Yaffe, “Numerical Holography”	Real-time numerical holography and characteristic evolution.
Andrade, “Holographic Lattices and Numerical Relativity”	Numerical methods for holographic lattices and transport.

For any numerical holography paper, inspect the validation section before trusting the physics. Look for convergence tests, residuals, DeTurck norm checks when applicable, Ward identities, thermodynamic consistency, and independence from coordinate/gauge artifacts.

Suggested reading routes

Route A: first serious pass through AdS/CFT

Read in this order:

1. Maldacena, GKP, Witten.
2. Aharony-Gubser-Maldacena-Ooguri-Oz review, sections on the canonical duality.
3. Skenderis on holographic renormalization.
4. Son-Starinets on real-time correlators.
5. Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi.
6. Harlow’s TASI lectures on bulk emergence.

This route prepares you to read most modern papers without getting lost.

Route B: correlators and CFT data

Read:

1. GKP and Witten.
2. Freedman-Mathur-Matusis-Rastelli.
3. Skenderis.
4. Penedones on Mellin amplitudes.
5. Heemskerk-Penedones-Polchinski-Sully.
6. Modern bootstrap/holography papers relevant to your target problem.

The key skill is translating between Witten diagrams and large-$N$ CFT data:

$$\{\Delta_i, C_{ijk}, \gamma_{n,\ell}, a_{n,\ell}\} \quad\longleftrightarrow\quad \{m_i, g_{ijk}, \text{bulk exchanges}, \text{loops}\}.$$

Route C: black holes, transport, and plasma

Read:

1. Witten on thermal AdS/CFT.
2. Son-Starinets.
3. Policastro-Son-Starinets.
4. Kovtun-Son-Starinets and Iqbal-Liu.
5. Fluid/gravity review.
6. Chesler-Yaffe if you want real-time numerical collisions.

This route is the most direct way to learn how horizons become dissipative field-theory physics.

Route D: quantum matter

Read:

1. Hartnoll lectures.
2. McGreevy many-body lectures.
3. Gubser and Hartnoll-Herzog-Horowitz on holographic superconductors.
4. Faulkner-Liu-McGreevy-Vegh on AdS$_2$ and Fermi surfaces.
5. Andrade-Withers and Donos-Gauntlett on momentum relaxation.

While reading, keep a field-theory hydrodynamics reference nearby. Many holographic finite-density phenomena are best understood as statements about conservation laws and symmetry breaking.

Route E: entanglement, reconstruction, and black-hole information

Read:

1. Ryu-Takayanagi and HRT.
2. Lewkowycz-Maldacena and FLM.
3. JLMS.
4. Almheiri-Dong-Harlow and Dong-Harlow-Wall.
5. Harlow’s Jerusalem lectures.
6. Penington, AEMM, AMMZ, and replica-wormhole papers.

This route is conceptually demanding because it mixes gravity, QFT, quantum information, and nonperturbative large-$N$ reasoning. Read slowly. The payoff is enormous.

How to turn a paper into a calculation

For any technical holography paper, try to extract one reproducible calculation in the following form.

Step 1: State the observable

Examples:

$$\langle \mathcal O(x)\mathcal O(0)\rangle, \qquad G^R_{J_xJ_x}(\omega,k), \qquad S_A, \qquad \langle W(C)\rangle, \qquad \Omega(T,\mu).$$

Step 2: State the bulk problem

Examples:

Observable	Bulk problem
Scalar two-point function	Solve a linear scalar wave equation in AdS.
Retarded conductivity	Solve a Maxwell perturbation with infalling horizon condition.
Entanglement entropy	Extremize an area or generalized entropy functional.
Heavy-quark potential	Minimize a string worldsheet ending on a rectangular loop.
Grand potential	Evaluate a renormalized Euclidean on-shell action.

Step 3: Identify the approximation

Typical approximations are:

$$N\to\infty, \qquad \lambda\to\infty, \qquad \omega/T\ll1, \qquad k/T\ll1, \qquad N_f/N\ll1, \qquad G_N\to0.$$

A paper that does not clearly state its approximation is not necessarily wrong, but you should supply the missing statement yourself before trusting the conclusion.

Step 4: Reproduce the simplest limit

Before attempting the full result, reproduce one limit:

• zero momentum,
• zero temperature,
• probe limit,
• near-boundary expansion,
• near-horizon expansion,
• hydrodynamic limit,
• large interval or small interval,
• linearized perturbation around a known solution.

Research taste often comes from knowing which limit is simple enough to expose the mechanism.

Common reading traps

Trap 1: treating all review statements as exact statements

Many review sentences are shorthand for a regime. “The bulk is classical gravity” usually means large $N$, large gap, and a two-derivative effective description, not exact equality.

Trap 2: missing ensemble dependence

At finite density, fixed $\mu$ and fixed $\rho$ are different problems. Boundary terms change. Thermodynamic potentials change. Stability can change.

Trap 3: confusing source and vev

Near-boundary expansions are not just asymptotic series. They encode the variational problem. Changing which mode is held fixed changes the dual theory.

Trap 4: forgetting contact terms

Momentum-space correlators often contain polynomial terms in $k^2$ or $\omega^2$. These are scheme-dependent contact terms unless protected by anomalies or Ward identities.

Trap 5: overgeneralizing bottom-up models

Bottom-up models are useful when treated as effective models. They become misleading when their outputs are presented as universal properties of quantum gravity or QCD.

Trap 6: reading islands as a full microscopic theory

Island calculations are profound semiclassical entropy calculations. They are not, by themselves, a complete decoding map for Hawking radiation or a complete microscopic description of every black-hole interior.

A compact “must know” bibliography by task

Task	First references
Compute a scalar two-point function	GKP, Witten, Freedman et al., Skenderis
Renormalize an asymptotically AdS action	de Haro-Skenderis-Solodukhin, Skenderis, Balasubramanian-Kraus
Compute a retarded Green function	Son-Starinets, Herzog-Son, Skenderis-van Rees
Compute $\eta/s$	Policastro-Son-Starinets, Kovtun-Son-Starinets, Iqbal-Liu
Study black-brane thermodynamics	Witten thermal AdS/CFT, AGMOO, standard black-hole thermodynamics references
Compute Wilson loops	Maldacena, Rey-Yee, Drukker-Gross-Ooguri
Add flavor	Karch-Katz, Kruczenski-Mateos-Myers-Winters
Study confinement models	Witten, Polchinski-Strassler, Erlich-Katz-Son-Stephanov, Karch-Katz-Son-Stephanov
Study finite density	Hartnoll, McGreevy, Faulkner-Liu-McGreevy-Vegh
Study holographic superconductors	Gubser, Hartnoll-Herzog-Horowitz, Herzog review
Study momentum relaxation	Andrade-Withers, Donos-Gauntlett, Hartnoll-Hofman
Compute RT/HRT surfaces	Ryu-Takayanagi, HRT, Lewkowycz-Maldacena
Understand bulk reconstruction	HKLL papers, Almheiri-Dong-Harlow, Dong-Harlow-Wall, Harlow TASI
Understand islands	Penington, AEMM, AMMZ, replica-wormhole papers
Do numerical holography	Headrick-Kitchen-Wiseman, Wiseman, Dias-Santos-Way, Chesler-Yaffe

Exercises

Exercise 1: Build a source-to-observable reading map

Choose one observable from the list below and identify three papers from this guide that you would read first:

$$\langle T_{\mu\nu}\rangle, \qquad G^R_{J_xJ_x}(\omega), \qquad S_A, \qquad \langle W(C)\rangle, \qquad \Omega(T,\mu).$$

For each paper, write one sentence beginning with “I read this paper for…”

Solution

One possible answer for $G^R_{J_xJ_x}(\omega)$ is:

1. Son-Starinets: I read this paper for the retarded prescription and infalling boundary condition.
2. Iqbal-Liu: I read this paper for the horizon/membrane interpretation of low-frequency transport.
3. Hartnoll’s lectures: I read this paper for the conductivity examples and condensed-matter interpretation.

For $S_A$, a natural answer is:

1. Ryu-Takayanagi: I read this paper for the classical area formula.
2. HRT: I read this paper for the covariant extremal-surface prescription.
3. Lewkowycz-Maldacena or FLM: I read this paper for the replica derivation and quantum corrections.

The important point is not the exact list. The important point is matching the paper to the calculational role it plays.

Exercise 2: Diagnose an approximation

A paper states that a strongly coupled gauge theory has $\eta/s=1/(4\pi)$. List at least four assumptions under which this statement is usually derived holographically.

Solution

A standard derivation assumes:

1. a large-$N$ limit, so that bulk loops are suppressed;
2. a large gap or large ‘t Hooft coupling, so that stringy higher-derivative corrections are suppressed;
3. a two-derivative Einstein gravity action in the relevant shear channel;
4. translationally invariant thermal equilibrium, usually represented by a black brane;
5. infalling/regular horizon boundary conditions for retarded response;
6. the hydrodynamic limit $\omega\to0$, $k\to0$ in the correct order.

Higher-derivative corrections, anisotropy, explicit translation breaking, finite coupling, or non-Einstein shear dynamics can change the result.

Exercise 3: Read a classic paper actively

Take the GKP paper or Witten’s AdS/holography paper. Extract the following data:

Question	Your answer
What is the boundary source?
What is the dual bulk field?
What is fixed at the AdS boundary?
What is differentiated to obtain correlators?
Which limit makes the bulk saddle classical?

Solution

For a scalar operator $\mathcal O$ dual to a bulk scalar $\phi$, the boundary source is the leading non-normalizable coefficient $\phi_{(0)}(x)$ in the near-boundary expansion. The bulk field $\phi$ is fixed asymptotically by $\phi_{(0)}$. The renormalized on-shell action $S_{\mathrm{ren}}[\phi_{(0)}]$ is differentiated with respect to $\phi_{(0)}$ to obtain connected correlators in the classical limit. The bulk saddle is classical when $N$ is large and, for a string embedding such as AdS$_5\times S^5$, the coupling is large enough that $\alpha'$ corrections are suppressed.

Exercise 4: Turn a bibliography into a research plan

Suppose you want to study charge transport in a finite-density holographic model with momentum relaxation. Propose a reading order of five papers and state what you would compute after each one.

Solution

A possible sequence is:

1. Hartnoll lectures: compute conductivity in a simple Maxwell black-brane model.
2. Son-Starinets: compute a retarded Green function using infalling boundary conditions.
3. Iqbal-Liu: derive the low-frequency membrane formula for a radially conserved flux.
4. Andrade-Withers: compute DC conductivity in the linear axion model.
5. Donos-Gauntlett: derive horizon DC conductivities in a more general setup.

After these, a good project-level extension is to add a scalar potential, a charged sector, or anisotropy, then test whether horizon formulae and Ward identities remain consistent.

Exercise 5: Identify a fragile conclusion

Pick one statement from the list and explain why it is not automatically universal:

1. Holographic plasmas have $\eta/s=1/(4\pi)$.
2. Soft-wall models confine.
3. An AdS$_2$ throat means the boundary theory is a strange metal.
4. Islands solve the black-hole information problem.

Solution

1. $\eta/s=1/(4\pi)$ is universal for a broad class of two-derivative Einstein gravity duals, but higher-derivative corrections and other modifications can change it.
2. A soft-wall model can produce discrete spectra and Regge-like behavior, but Wilson-loop confinement depends on the string-frame geometry and the behavior of the effective string tension.
3. An AdS$_2$ throat gives semi-local IR scaling and often controls low-frequency response, but strange-metal phenomenology requires additional statements about momentum relaxation, charge transport, scaling regimes, and comparison to experiment.
4. Islands reproduce Page-curve behavior in semiclassical entropy calculations in controlled setups, but they do not automatically provide a microscopic decoding map or settle every question about black-hole interiors.

The final habit

The best readers of AdS/CFT papers are bilingual. They can read a statement in the CFT language and translate it into geometry, then translate the geometry back into a statement about sources, vevs, correlators, entropies, or spectra.

Whenever a paper feels obscure, write the dictionary line first:

$$\text{boundary question} \quad\longleftrightarrow\quad \text{bulk boundary-value problem}.$$

Then ask what approximation makes that boundary-value problem tractable. Most of the literature becomes much less mysterious after that.