Nonperturbative String- and M-Theory Definition Proposals

A nonperturbative definition must say which quantum system is defined and how spacetime observables are recovered from it. This chapter compares matrix models, string field theories, and holographic proposals through their mathematical objects and required limits; agreement in a controlled sector does not establish every part of a proposed completion.

Enter this chapter

Begin with Nonperturbative Definition Proposals: Objects, Evidence, and Falsifiers to compare the proposals on common scientific questions.

Helpful background. Completion criteria distinguishes exact rules from asymptotic series; decoupling limits supplies the perturbative starting point.

Topics

1. Nonperturbative Definition Proposals: Objects, Evidence, and Falsifiers — Specify the quantum object and the recovery claim separately.
2. String and M-Theory Duality Webs and Parameter Maps — Translate parameters and sectors across string and M-theory descriptions.
3. BFSS Matrix Quantum Mechanics and M-Theory Conjectures — Study the matrix Hamiltonian proposed for a light-cone M-theory limit.
4. BMN Plane-Wave Matrix Model and Controlled Sectors — Use a mass-deformed model to test controlled plane-wave sectors.
5. IKKT Type-IIB Matrix Model and Emergent-Spacetime Claims — Examine spacetime emergence from a matrix integral without microscopic time.
6. Matrix-String Constructions and Second-Quantized Strings — Recover string joining and splitting from a two-dimensional gauge theory.
7. Open String Field Theory and Tachyon Dynamics — Test open-string dynamics and unstable-brane decay off shell.
8. Covariant and Closed String Field Theory — Organize closed-string interactions with gauge-consistent vertices.
9. AdS/CFT as a Conditional Nonperturbative Definition — State the assumptions under which a boundary theory defines a bulk sector.
10. Background Dependence, Background Independence, and Emergence — Distinguish fixed asymptotic data from a chosen perturbative background.
11. Numerical Matrix Evidence, Classical-Spacetime Recovery, and Limits — Separate numerical agreement from the extrapolations needed for spacetime recovery.

How the ideas fit together

BFSS illustrates the separation between a defined model and its interpretation. Supersymmetric matrix quantum mechanics supplies degrees of freedom and a Hamiltonian; recovering uncompactified M-theory requires a specified large-$N$ limit and a map to spacetime quantities. The original proposal tests supergraviton states and a restricted scattering regime, while explicitly leaving broader recovery questions open Banks et al. 1997, §§ 3–4.

This distinction guides numerical tests too. Removing a regulator establishes a property of the matrix system. A gravitational interpretation additionally requires the dictionary and the limits connecting that property to the target spacetime observable.

Claim-domain comparison

Compare the assumptions and limits of these representative conclusions.

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Representative claim domains and validity boundaries for Nonperturbative String- and M-Theory Definition Proposals

Claim object	State, ensemble, and conventions	Approximation, status, and evidence timing	Uncertainty and counterevidence	Falsifier	Failure condition	Licensed conclusion
matrix quantum mechanics	Declare large-N limit and compactification sector; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: defining variables and action → Hamiltonian or path integral → observable and sector map → spacetime recovery tests → typed definition claim. Sources are cited on the destination page; literature checked through 10 August 2026.	Track omitted corrections, alternate branches, and competing definitions. A failed “spectrum and scattering benchmarks” check is counterevidence to the promoted claim.	A spectrum or scattering benchmark in the claimed target sector disagrees after the specified large-N limit and cutoff errors are controlled.	Promoting a candidate sector definition to manifest covariant completeness.	a candidate M-theory sector
matrix or string field model	Declare gauge fixing, background, and observables; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: defining variables and action → Hamiltonian or path integral → observable and sector map → spacetime recovery tests → typed definition claim. Sources are cited on the destination page; literature checked through 10 August 2026.	Track omitted corrections, alternate branches, and competing definitions. A failed “unitarity and spacetime-recovery tests” check is counterevidence to the promoted claim.	A gauge-invariant amplitude fails the unitarity relation or spacetime-recovery benchmark actually claimed for the declared background and sector.	Promoting model-defined amplitudes or states to a definition of all nonperturbative backgrounds.	the model-defined amplitudes or states
AdS/CFT as definition	Declare exact boundary theory and global data; use the volume conventions unless the page states a local replacement.	Model-specific calculation or conditional result. Control chain: defining variables and action → Hamiltonian or path integral → observable and sector map → spacetime recovery tests → typed definition claim. Sources are cited on the destination page; literature checked through 10 August 2026.	Track omitted corrections, alternate branches, and competing definitions. A failed “bulk dictionary completeness” check is counterevidence to the promoted claim.	Within the claimed AdS domain, a required observable or global sector has no image under the proposed complete map, or mapped algebra relations disagree.	Extending a definition of one AdS sector to arbitrary quantum gravity.	conditional definition of its AdS sector

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Review the chapter

A simulation agrees with a black-hole thermodynamic prediction at several finite matrix sizes. What separates this result from a complete nonperturbative definition of gravity?

Solution

The agreement tests one observable in a specified regime. Regulator removal, finite-size and limit-order control must first support the matrix-model result. The claim about gravity additionally requires a justified observable map and recovery of the proposed sectors; one thermodynamic curve cannot establish those independently.

Where to go next

Continue to Holographic Renormalization and Radial Dynamics for a concrete calculation within the AdS source dictionary.

References

• Banks, T., Fischler, W., Shenker, S. H., and Susskind, L. (1997), “M Theory as a Matrix Model: A Conjecture,” Physical Review D 55, 5112–5128. arXiv:hep-th/9610043.