AdS/CMT Correspondence¶

Model selected observables of a strongly coupled condensed-matter quantum field theory with a tractable higher-dimensional gravitational system, using an explicit bulk-boundary dictionary and carrying predictions back only within the holographic model's declared validity envelope.

Version: v2 · 2026-09-06 · History
Domain-specific #: 1246
Origin domain: theoretical physics
Subdomain: holographic condensed matter
Aliases: Anti-de Sitter/condensed matter theory correspondence, Anti-de Sitter condensed matter correspondence, Holographic condensed matter

Core Idea¶

AdS/CMT correspondence is a holographic modeling framework for selected strongly coupled condensed-matter systems. It begins with a quantum field theory or low-energy many-body target for which ordinary quasiparticle or perturbative methods are inadequate, chooses a higher-dimensional asymptotically anti-de Sitter gravitational model, fixes a bulk-boundary dictionary between fields and operators, solves the bulk boundary-value problem, and translates the result back into boundary thermodynamics, correlation functions, phases, or transport. Its point is not that a literal laboratory material is secretly a black hole. Its point is that gauge/gravity duality can turn certain strong-coupling questions into classical or semiclassical gravitational calculations in a controlled model.^[1]^[2]^[3]

For a bulk field \(\phi\) dual to a boundary operator \(\mathcal O\), the near-boundary behavior in a standard quantization has the schematic form

\[ \phi(z,x)=z^{d-\Delta}\phi_{(0)}(x)+z^{\Delta}A(x)+\cdots, \qquad m^2L^2=\Delta(\Delta-d). \]

The leading coefficient \(\phi_{(0)}\) is interpreted as a source, while the properly renormalized subleading response determines \(\langle\mathcal O\rangle\), subject to normalization and quantization conventions. A bulk gauge potential can encode boundary chemical potential and charge density; a black-brane horizon supplies temperature and dissipation; ingoing horizon conditions select retarded response. Conductivity is then obtained from the retarded current correlator through a Kubo relation, schematically \(\sigma(\omega)=G^R_{J_xJ_x}(\omega,0)/(i\omega)\), with contact terms and normalizations fixed by the chosen theory.^[2]^[4]

The locked identity is:

a declared strongly coupled boundary target + a tractable asymptotically AdS bulk model + an explicit field/operator and source/response dictionary + boundary and horizon conditions that define the state and causal observable + a bulk calculation + a translation back to boundary quantities + a validity ledger covering large-N, coupling, symmetry, conservation, translation breaking, and top-down versus bottom-up status -> a holographic prediction or controlled model result for condensed-matter thermodynamics, phase structure, spectra, or transport.

This identity is narrower than the AdS/CFT conjecture and more structured than a research-area label. A paper is not an instance merely because it discusses strings and condensed matter. It must expose enough of the dictionary and validity envelope for a reader to audit how the gravitational calculation bears on the boundary observable.

Structural Signature¶

Sig role-phrases:

the strongly coupled boundary target — a quantum critical, compressible, superconducting, superfluid, strange-metal, or related many-body system posed as a field-theoretic problem
the observable contract — the thermodynamic quantity, order parameter, Green function, spectral feature, or transport coefficient the model is built to compute
the bulk gravitational model — an asymptotically AdS action, matter content, couplings, and spacetime ansatz chosen to encode the desired boundary ingredients
the holographic dictionary — an explicit correspondence between bulk fields and boundary operators, sources and responses, horizon data and state variables
the state-setting boundary conditions — asymptotic data such as temperature, chemical potential, external source, or deformation together with regularity or ingoing conditions at the horizon
the tractable bulk solution — an analytic or numerical classical/semi-classical solution and its perturbations
the extraction rule — holographic renormalization and causal-response prescription converting near-boundary coefficients or on-shell action variations into boundary quantities
the strong-to-tractable leverage — the use of weakly curved classical gravity to access a boundary regime that is strongly coupled and often lacks quasiparticles
the validity ledger — large-\(N\), coupling, symmetry, conservation, homogeneity, field-content, and top-down/bottom-up assumptions that delimit the claim
the boundary interpretation — the final statement about a condensed-matter phase, scaling law, response function, or transport pattern, kept distinct from direct material identification
the comparison test — checks against field-theory constraints, hydrodynamics, sum rules, known limits, numerics, or experiment that determine what the model has actually learned

Recognition test. Ask six questions. What is the boundary theory or effective target? Which boundary observable is sought? What bulk field or geometry represents each load-bearing ingredient? Which coefficient or on-shell variation yields the observable? Which boundary and horizon conditions define the state and retarded response? Which assumptions license carrying the result back? If a proposal only says “black holes resemble strange metals,” it fails. If it supplies an operational dictionary, solves a specified bulk problem, extracts a boundary observable, and states the validity envelope, it instantiates AdS/CMT even when the model is deliberately bottom-up and not claimed to be a microscopic dual of a real material.

What It Is Not¶

Not merely a field or community label. The node denotes the reusable model-to-observable workflow inside the field, not every paper, workshop, or topic called holographic condensed matter.
Not a claim that known materials have established exact gravitational duals. Many AdS/CMT models are bottom-up effective constructions; agreement with a scaling form does not identify a unique microscopic material dual.
Not loose analogy. A black hole used as a metaphor for dissipation lacks the bulk action, field/operator map, state conditions, and extraction rule required here.
Not the whole AdS/CFT correspondence. AdS/CFT is the parent gauge/gravity duality. AdS/CMT selects condensed-matter questions, model ingredients, observables, and validation burdens.
Not ordinary weak-coupling perturbation theory. The leverage comes from a dual description that may be classical when the boundary is strongly coupled, not from expanding in the boundary interaction strength.
Not automatically predictive for a laboratory compound. Bottom-up models can reveal mechanisms, constraints, or universality-compatible behavior without fixing material-specific numbers.
Not a correspondence-principle limit. The live Correspondence Principle prime concerns a new theory reproducing an older theory in a limiting regime. Holographic duality relates two descriptions, not necessarily an old and new theory joined by a limit.
Not a gauge choice or gauge invariance alone. Gauge fields and symmetries are ingredients of many models, but the abstraction is the complete bulk-boundary modeling route.
Not universality alone. Universal critical behavior may make a holographic model informative across microscopic systems, but universality does not itself supply the bulk dictionary or computation.
Not evidence-free curve fitting. A model should satisfy theoretical constraints and expose which input choices control the fitted response; flexible bulk couplings can otherwise reproduce shapes without explanatory discrimination.

Scope of Application¶

AdS/CMT lives in theoretical condensed-matter physics at the interface with quantum field theory and gravitational holography. Its scope is broad within that interface but bounded by the availability and credibility of a holographic model.

Quantum critical matter. Finite-temperature dynamics and transport near scale-invariant strongly coupled fixed points can be encoded by black-brane backgrounds and their perturbations.^[3]
Compressible quantum matter. Bulk gauge fields and charged horizons model systems at nonzero density, including candidate non-Fermi-liquid and strange-metal regimes.^[5]
Superconductors and superfluids. Charged bulk matter can condense below a critical temperature, yielding a boundary order parameter and characteristic conductivity response.^[6]
Hydrodynamics and transport. Horizon regularity, conserved fluxes, and linear response give diffusion, viscosity, electric, thermal, and thermoelectric coefficients in declared models.^[2]^[4]
Translation breaking and momentum relaxation. Lattices, disorder, axion fields, or other deformations can remove the infinite translationally invariant DC response and expose finite transport.
Nonequilibrium dynamics. Time-dependent geometries can model quenches, thermalization, and relaxation when the bulk initial-boundary problem is well posed.
Entanglement and information-sensitive probes. Geometric prescriptions can be used to study entanglement structure, although that wider holographic program is not exhausted by AdS/CMT.

The method is strongest when the question concerns robust collective behavior, scaling, or transport in a regime plausibly represented by a large-\(N\), strongly coupled theory. It is weakest when microscopic lattice chemistry, a small number of degrees of freedom, quasiparticle detail, or uncontrolled stringy/quantum-gravity corrections dominate the observable.

Clarity¶

Clarity begins by separating four levels.

The boundary target is the field theory or many-body phenomenon of interest.
The bulk model is the gravitational representation selected to calculate it.
The dictionary says what bulk variables mean on the boundary.
The material interpretation says whether the result is exact for a specified theory, generic across a class, qualitatively suggestive, or compared with a real system.

The levels must not be collapsed. A classical bulk solution can be an exact leading-order result for its declared holographic boundary theory while remaining only a model for a material. Conversely, the absence of a known microscopic top-down embedding does not make every bottom-up result meaningless; it changes the epistemic status and the tests required.

The source/response distinction is equally important. Changing the leading boundary coefficient generally changes the theory or externally applied field; reading the subleading coefficient gives a response. Setting a scalar source to zero while obtaining a nonzero expectation value distinguishes spontaneous from explicit symmetry breaking. At a horizon, regularity is appropriate in Euclidean calculations, while ingoing behavior selects a retarded real-time correlator. Confusing these choices changes the physical question rather than merely its notation.^[2]^[4]

Finally, every claim should name its approximation order. Classical two-derivative gravity typically represents a large-\(N\), strong-coupling limit. Higher-derivative terms encode finite-coupling corrections; bulk loops encode \(1/N\) effects. “Holography predicts” is incomplete unless it says for which model and at which order.

Manages Complexity¶

Strongly interacting quantum matter has too many coupled degrees of freedom for a simple quasiparticle description. AdS/CMT manages that complexity by replacing a boundary many-body calculation with a geometric boundary-value problem. Symmetry, conservation laws, temperature, density, and operator content become choices of bulk fields, action terms, geometry, and boundary conditions. The resulting model can reduce a difficult correlation problem to solving coupled ordinary or partial differential equations.

The framework also modularizes inference. Equilibrium comes from a background solution and renormalized on-shell action. Phase instability comes from a bulk mode becoming unstable or developing hair. Linear response comes from perturbing the background, imposing causal horizon data, and reading near-boundary coefficients. DC transport can sometimes be expressed in horizon data; frequency-dependent transport requires integrating perturbations across the bulk. Each module has a distinct failure surface.

This organization turns disagreement into diagnosis. If a conductivity lacks a finite Drude-like width, check whether translation invariance conserves momentum. If an order parameter appears with a nonzero source, distinguish explicit from spontaneous breaking. If a scaling exponent changes when a higher-derivative term is added, the result was not protected at leading order. If several unrelated bulk actions fit the same boundary curve, the observable underdetermines the model. The abstraction makes these questions visible before a black-hole calculation is treated as a material prediction.

Abstract Reasoning¶

The central move is solve on the tractable side, interpret on the target side. Let \(Z_{\mathrm{QFT}}[\phi_{(0)}]\) be the boundary generating functional with source \(\phi_{(0)}\). In the classical gravity regime,

\[ Z_{\mathrm{QFT}}[\phi_{(0)}]\approx \exp\!\left[-S^{\mathrm{ren}}_{\mathrm{bulk,on\text{-}shell}}[\phi\to\phi_{(0)}]\right]. \]

Functional differentiation yields one- and two-point functions after holographic renormalization. Real-time response adds a causal prescription. The reasoning is not “gravity causes the material.” It is “the correspondence equates generating data for the declared model, so a bulk calculation licenses a boundary inference.”^[1]^[4]

Model construction then becomes a constrained inverse problem. Start from required boundary symmetries and observables. Choose the smallest bulk content that can encode them. Derive, rather than merely name, the relevant source/response map. Solve and check regularity. Test Ward identities, thermodynamic consistency, spectral positivity where applicable, hydrodynamic limits, and sum rules. Only then compare with a condensed-matter phenomenon.

Counterfactual reasoning is especially useful. If momentum relaxation is removed, should DC conductivity diverge? If the scalar charge is set to zero, should the superconducting instability disappear? If the boundary source is turned on, does the transition become explicit? If the bulk curvature becomes string scale, does the classical approximation remain credible? A model that cannot answer these role-based counterfactuals has not supplied a usable correspondence.

Knowledge Transfer¶

Within holographic many-body physics, the whole mechanism transfers literally. One can change the boundary phase, dimension, density, symmetry, or observable while retaining the same role package: choose a bulk model, define the dictionary, impose boundary/horizon conditions, solve, extract, and audit validity. That is why the node is a reusable domain abstraction rather than one black-hole example.

Outside physics, the thin skeleton resembles translating a hard problem into a dual representation, solving there, and mapping back. Optimization duals, Fourier methods, and latent-state models can share that shape. But calling them AdS/CMT would be metaphorical because they have no asymptotically AdS bulk, field/operator dictionary, holographic renormalization, or horizon prescription. The portable lessons belong to the live Representation and Duality primes. The named mechanism stays in holographic condensed matter.

Examples¶

Canonical: a minimal holographic superconductor¶

Take Einstein gravity in asymptotically AdS spacetime coupled to a Maxwell field and a charged scalar. The normal finite-density phase is represented by a charged black brane with vanishing scalar. Below a critical temperature the scalar can develop a nonzero profile. With its boundary source set to zero, the normalizable coefficient gives a spontaneous boundary condensate. Perturbing the bulk gauge field by \(\delta A_x(z)e^{-i\omega t}\), imposing ingoing behavior at the horizon, and reading its near-boundary response yields the boundary optical conductivity. Hartnoll, Herzog, and Horowitz found a critical transition, infinite DC conductivity in the translationally invariant idealization, and a frequency-dependent gap-like response.^[6]

Mapped back: the finite-density field theory is the boundary target; the Einstein-Maxwell-scalar action is the bulk model; scalar and gauge-field coefficients form the dictionary; source-free asymptotics and ingoing horizon behavior are the state-setting conditions; the condensate and conductivity are the observable contract; and the absence of momentum relaxation is part of the validity ledger, not a hidden prediction for dirty materials.

Applied / In Practice: quantum-critical transport model¶

Suppose a theorist wants the low-frequency conductivity of a strongly coupled compressible state without stable quasiparticles. They specify the conserved \(U(1)\) current, density, temperature, and whether momentum relaxes. A charged black-brane background encodes the equilibrium state; bulk gauge and metric perturbations encode current and momentum response. Ingoing horizon conditions choose the retarded correlator. Near-boundary coefficients yield the current-current Green function, and the Kubo formula yields conductivity. If translations remain exact, the momentum overlap can produce a zero-frequency singular contribution; a finite experimental DC value therefore requires a translation-breaking channel or an explicit statement that only an incoherent component is being compared. Reviews by Sachdev and by Hartnoll, Lucas, and Sachdev use this workflow to organize quantum-critical and compressible transport while emphasizing the distinction between solvable holographic theories and real materials.^[3]^[5]

Mapped back: the non-quasiparticle state is the strongly coupled target; charge and momentum response define the observable contract; the charged black brane and perturbations supply the tractable bulk solution; the Kubo extraction supplies the boundary interpretation; and translation symmetry is a load-bearing entry in the validity ledger.

Worked intervention — a suspicious conductivity match. If a bottom-up model matches the optical-conductivity curve but its DC limit and spectral weight are wrong, first test the dictionary and normalization, then the Ward identity and sum rule, then momentum conservation and translation breaking. Vary the irrelevant bulk couplings that were tuned to the curve. If many choices preserve the match while changing other observables, the fit is underdetermined. Add a discriminating observable—thermoelectric response, density dependence, or a quasinormal-mode pole—and narrow the claim from “the material is holographic” to the model-supported mechanism or scaling relation.

Structural Tensions¶

T1: Tractability versus microscopic fidelity. A simple classical bulk can make a strong-coupling problem calculable precisely because it suppresses microscopic detail. Adding realistic fields and couplings may improve fidelity while destroying analytic control. Diagnostic: Which omitted microscopic feature could change the target observable, and is the current claim universal enough to survive its omission?

T2: Exact duality versus phenomenological model. Top-down constructions can supply a firmer dictionary but often describe theories unlike real materials; bottom-up models can target desired phenomenology but may lack a known ultraviolet completion. Diagnostic: Is the result exact for a specified boundary theory, generic across a controlled class, or phenomenological for a material?

T3: Strong-coupling leverage versus large-\(N\) distortion. Classical gravity opens strongly coupled regimes but generally relies on large \(N\) and strong coupling, which can suppress fluctuations important in finite-component condensed matter. Diagnostic: Which conclusion is protected at leading order, and which could be reversed by \(1/N\) or finite-coupling corrections?

T4: Universal structure versus flexible fitting. Holographic models can reveal robust constraints and scaling, yet flexible bulk actions can fit many curves. Diagnostic: Does the model predict an independent observable or only reproduce the quantity used to tune it?

T5: Horizon dissipation versus boundary mechanism. A horizon efficiently produces causal relaxation and entropy, but a material's dissipation may arise from disorder, phonons, umklapp, or other microscopic channels. Diagnostic: Which boundary conservation law and relaxation channel corresponds to the chosen horizon or translation-breaking structure?

T6: Geometric intuition versus dictionary discipline. Geometric pictures make collective dynamics intelligible, but literalizing the picture can turn a dual representation into a causal story. Diagnostic: Can every physical claim be restated as a boundary observable derived through the dictionary without saying the material contains a spacetime horizon?

T7: Autonomy versus reduction. Representation and Duality capture the portable skeleton, but neither supplies asymptotically AdS dynamics, source/response coefficients, horizon causality, or strong-coupling condensed-matter interpretation. Diagnostic: If the bulk action, field/operator dictionary, and horizon/boundary extraction rules are removed, can the parent primes still identify a valid AdS/CMT calculation? If not, the domain node remains autonomous.

Structural–Framed Character¶

AdS/CMT Correspondence is mixed-structural. Its internal inferential machinery is highly formal, while its identity is pinned to a specialist research program and a particular family of physical representations.

Vocabulary travels (0.75). Model, source, response, duality, and observable travel widely; bulk, boundary, asymptotically AdS, black brane, and holographic renormalization do not.

Evaluative weight (0.0). The framework is neither praise nor condemnation. A model can be valid, limited, or misleading, but the abstraction itself is neutral.

Institutional origin (0.25). The method arose in a scientific tradition and uses conventional dictionaries, yet results follow from declared actions and boundary conditions rather than institutional authority.

Human-practice boundedness (0.25). The correspondence is a theory-building practice, but once a model is specified its equations and extracted observables are not determined by social judgment.

Import versus recognition (0.75). Holographic theorists recognize the same bulk-boundary workflow across superconductors, quantum criticality, and transport. Applying the name to ordinary dual modeling outside gauge/gravity physics imports an analogy.

The portable skeleton is a representation solved through a dual description under a faithfulness and validity contract. Its character: structurally rigorous inside holographic condensed matter, but inseparable from the specialist physics that gives its dictionary meaning.

Structural Core vs. Domain Accent¶

This section explains why AdS/CMT Correspondence is domain-specific rather than a prime.

What is skeletal. A difficult target is represented in a second formal system; a correspondence maps inputs and observables between the systems; computation occurs where it is tractable; and the result is translated back under explicit scope conditions. Representation carries the target-medium-faithfulness structure. Duality carries the licensed cross-side inference. That thin structure appears in optimization, transforms, and other formal sciences.

What is domain-bound. The actual mechanism requires a boundary quantum field theory, a higher-dimensional asymptotically AdS bulk, the gauge/gravity field/operator dictionary, source and response asymptotics, holographic renormalization, black-brane thermodynamics, causal horizon conditions, and a large-\(N\)/strong-coupling expansion. The diagnostic questions concern current operators, stress tensors, chemical potential, condensates, quasinormal modes, and transport. Remove those commitments and the method is no longer AdS/CMT; it is generic dual modeling.

Why this does not clear the prime bar. Literal transfer across unrelated substrates fails. A supply-chain model can be solved in a dual representation, but it has no bulk spacetime whose near-boundary coefficients encode operator expectation values. The same words would be metaphorical. The cross-domain reach belongs to Representation and Duality, while the named workflow remains a specialist instance whose validity depends on gravitational and quantum-field-theoretic conditions.

AdS/CMT Correspondence instantiates Representation. The boundary theory is the target, the gravitational bulk is the representing medium, the dictionary states which structure is preserved, and the validity ledger supplies the faithfulness specification. This is the closest genus.

It presupposes Duality in the strict sense. Gauge/gravity correspondence licenses calculation on the bulk side and inference on the boundary side. The domain node adds the condensed-matter target, model-building workflow, observable extraction, and approximation audit.

Gauge Invariance / Gauge Symmetry and Universality are important related primes, but neither is universal enough to be a direct parent. Many models use bulk gauge symmetry to encode a conserved current, and many interpretations target universal infrared behavior, yet the framework can be stated without making either the defining operation. Correspondence Principle is declined because recovering an older theory as a limit is different from using dual descriptions.

Relationships to Other Abstractions¶

Current abstraction AdS/CMT Correspondence Domain-specific

Parents (2) — more general patterns this builds on

AdS/CMT Correspondence is a kind of Representation Prime

AdS/CMT Correspondence instantiates Representation. The boundary theory is the target, the gravitational bulk is the representing medium, the dictionary states which structure is preserved, and the validity ledger supplies the.
AdS/CMT Correspondence presupposes Duality Prime

AdS/CMT Correspondence instantiates Representation. The boundary theory is the target, the gravitational bulk is the representing medium, the dictionary states which structure is preserved, and the validity ledger supplies the.

Hierarchy paths (2) — routes to 2 parentless roots

AdS/CMT Correspondence → Representation → Abstraction

Show alternative path (1)

Neighborhood in Abstraction Space¶

AdS/CMT Correspondence sits in a sparse region of the domain-specific corpus (86^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (1565 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08

Not to Be Confused With¶

AdS/CFT correspondence. The parent gauge/gravity duality covers a much wider class of questions. AdS/CMT is its condensed-matter modeling program and workflow. Tell: Is the target a condensed-matter or many-body observable with a domain-specific interpretation burden?
Holographic principle. The broad principle concerns encoding gravitational bulk information on a lower-dimensional boundary; it does not specify the CMT model-building sequence. Tell: Are source/response and observable-extraction rules actually supplied?
Correspondence Principle. That prime requires recovery of an older description in a limit. Tell: Is the relation a limiting reduction, or a dual bulk-boundary dictionary?
Gauge invariance. Gauge redundancy constrains representations and conservation, but it does not by itself give a gravitational dual. Tell: Can the claimed result be obtained from gauge symmetry without solving a bulk-boundary problem?
Universality. Universality explains why microscopic differences can share macroscopic behavior. Tell: Does the claim rest on coarse-grained shared exponents alone, or on a holographic calculation?
Dynamical mean-field theory. DMFT maps a lattice many-body problem to a self-consistent impurity problem; it is a different strong-coupling representation with different approximations. Tell: Is the auxiliary problem an impurity with self-consistency or an asymptotically AdS gravitational bulk?
Lattice quantum Monte Carlo. QMC samples a discretized path integral and may face sign problems; it does not use a bulk gravitational dual. Tell: Is the observable estimated statistically from configurations or extracted from classical bulk fields?
Black-hole analogy. Analogy may be pedagogically useful but carries no licensed prediction. Tell: Is there an action, dictionary, boundary condition, and extraction rule?
A microscopic theory of a real material. A bottom-up holographic model can organize collective behavior without deriving from atomic constituents. Tell: Are material-specific Hamiltonian parameters derived, or only a universality-compatible response modeled?

References¶

[1] Maldacena, J. M. "The Large N Limit of Superconformal Field Theories and Supergravity". Advances in Theoretical and Mathematical Physics 2, 231–252 (1998). Foundational gauge/gravity duality and its large-\(N\), supergravity regime. registry ↩a ↩b

[2] Hartnoll, S. A. "Lectures on Holographic Methods for Condensed Matter Physics". Classical and Quantum Gravity 26, 224002 (2009). Bulk-boundary dictionary, thermodynamics, transport, and superconductivity methods. registry ↩a ↩b ↩c ↩d

[3] Sachdev, S. "What Can Gauge-Gravity Duality Teach Us About Condensed Matter Physics?". Annual Review of Condensed Matter Physics 3, 9–33 (2012). Authoritative scope and limitations for conformal and compressible quantum matter. registry ↩a ↩b ↩c

[4] Son, D. T., and Starinets, A. O. "Minkowski-Space Correlators in AdS/CFT Correspondence: Recipe and Applications". Journal of High Energy Physics 2002(09), 042 (2002). Ingoing-horizon prescription for retarded boundary correlators. registry ↩a ↩b ↩c ↩d

[5] Hartnoll, S. A., Lucas, A., and Sachdev, S. Holographic Quantum Matter. MIT Press (2018; preprint 2016). Authoritative synthesis of holographic states, quantum criticality, and transport. registry ↩a ↩b

[6] Hartnoll, S. A., Herzog, C. P., and Horowitz, G. T. "Building a Holographic Superconductor". Physical Review Letters 101, 031601 (2008). Primary charged-scalar holographic-superconductor construction and conductivity result. registry ↩a ↩b