Top-Down, Bottom-Up, and UV-Completion Claim Contracts

“Top-down,” “consistent truncation,” “bottom-up,” and “UV complete” answer different questions. A top-down embedding fixes microscopic charge, spectrum, and parameter data in a parent construction. A consistent truncation gives exact uplift within specified parent equations. A bottom-up model parametrizes an infrared sector. None of these labels alone proves that a model is the unique microscopic theory of an observed system.

Required background. Nonperturbative definition and completion criteria supplies the stronger standard for a complete theory. Stringy and quantum corrections supplies the expansion limits inherited by gravitational models.

Helpful background. Nondecoupling effects and matching validation supplies EFT validation tests. Claim, evidence, replication, and retraction supplies evidence discipline for quantitative fits.

Four construction classes

An explicit brane compactification is top-down when the higher-dimensional theory, quantized fluxes, compact manifold, boundary conditions, and dictionary are specified. It supports claims about that background in controlled $g_s$, $\alpha'$, curvature, and $N$ regimes. It need not provide a nonperturbative definition outside those regimes; the distinction is explicit in the standard AdS/CFT review Aharony et al. 2000.

A consistent truncation asserts that solutions of a retained lower-dimensional action uplift to the stated parent equations. It establishes embeddability, not that omitted string or quantum corrections vanish and not that every parent solution is represented.

A bottom-up action chooses fields and couplings compatible with desired symmetries and phenomenology. It can reveal universal consequences of horizons, conservation laws, or scaling, and it can fit data, as illustrated by the explicit scope analysis of AdS/QCD models Erlich 2014. Its Wilson coefficients are hypotheses to be constrained; without an embedding, their allowed correlations and ultraviolet behavior remain unknown.

A UV-completion claim requires more: a well-defined microscopic object, complete observables and global data, regulator independence or an exact construction, and recovery of the claimed low-energy sectors. “Has a classical solution” and “has no visible instability in one truncation” do not meet that standard. Analyticity and causality can even exclude apparently acceptable low-energy coefficients Adams et al. 2006.

First application: two charged black-brane models

Compare a flux compactification whose consistent sector contains an Einstein–Maxwell–scalar action with a phenomenological action of the same form fitted to a condensed-matter conductivity. In the top-down case, charge normalization, scalar potential, Chern–Simons terms, and allowed boundary conditions descend from the parent theory; uplift verifies every classical solution in the retained sector. Predictions remain limited by large $N$, weak curvature, small $g_s$, and the observables captured by the truncation.

In the bottom-up case, the fit can establish that a specified response function is well described over a frequency and temperature window. It may also demonstrate universality if the result is insensitive to allowed couplings. It cannot identify the laboratory material with a particular string compactification, infer a unique operator spectrum, or establish UV completion. Matching more observables with one parameter set raises confidence but does not change the logical type of the claim.

Adversarial control: a successful fit with incompatible completions

Construct two bulk actions that have the same near-horizon geometry and fit the same low-frequency conductivity, but differ in higher-derivative coefficients and additional charged states. They agree inside the calibration window and disagree at higher frequency or in a different correlator. The original fit therefore underdetermines the microscopic completion. A top-down embedding of one action would constrain its coefficients, but would still not show that nature selected that embedding.

The evidence ceiling should be stated directly: embeddable classical sector, controlled EFT prediction, universal infrared relation, phenomenological fit, candidate microscopic dual, or conditional nonperturbative definition. Each requires different falsifiers. The next chapter begins with a comparison of nonperturbative proposals and asks which, if any, satisfy the last category.

The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.

For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.

References

• Adams, A., Arkani-Hamed, N., Dubovsky, S., Nicolis, A., and Rattazzi, R. (2006), “Causality, Analyticity and an IR Obstruction to UV Completion,” Journal of High Energy Physics 2006(10), 014. arXiv:hep-th/0602178.
• Aharony, O., Gubser, S. S., Maldacena, J. M., Ooguri, H., and Oz, Y. (2000), “Large $N$ Field Theories, String Theory and Gravity,” Physics Reports 323, 183–386. arXiv:hep-th/9905111.
• Erlich, J. (2014), “How Well Does AdS/QCD Describe QCD?,” International Journal of Modern Physics A 29, 1430002. arXiv:1401.0008.