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Taming the Landscape of Effective Theories

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arxiv 2112.08383 v1 pith:HPTOX2AM submitted 2021-12-15 hep-th

Thomas W. Grimm This is my paper · ORCID
classification hep-th
keywords theorieseffectivegeometrytametamenessconjecturedefinableflux
verification ladder T0 review T1 audit T2 compute T3 formal
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We introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, we propose a Tameness Conjecture that states that all valid effective theories are labelled by a definable parameter space and must have scalar field spaces and coupling functions that are definable using the tame geometry built from an o-minimal structure. We give a brief introduction to tame geometry and describe how it restricts sets, manifolds, and functions. We then collect evidence for the Tameness Conjecture by studying various effective theories arising from string theory compactifications by using some recent advances in tame geometry. In particular, we will exploit the fact that coset spaces and period mappings are definable in an o-minimal structure and argue for non-trivial tameness results in higher-supersymmetric theories and in Calabi-Yau compactifications. As strongest evidence for the Tameness Conjecture over a discrete parameter space, we then discuss a recent theorem stating that the locus of self-dual flux vacua of F-theory admits a tame geometry even if one allows for any flux choice satisfying the tadpole constraint. This result implies the finiteness of self-dual flux vacua in F-theory.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape

    hep-th 2026-01 conditional novelty 7.0 of 10

    Effective field theories consistent with quantum gravity are conjectured to have uniformly bounded 'tame complexity', a quantitative measure of the information needed to specify them.

  2. A finite 6d supergravity landscape from anomalies

    hep-th 2025-07 conditional novelty 7.0 of 10

    Local and Dai-Freed global anomaly cancellation implies T ≤ 3003 and a finite 6d non-abelian supergravity landscape, with the extremal model [E8 x F4 x (G2 x SU(2))^2]^273.

  3. Deep observations of the Type IIB flux landscape

    hep-th 2025-01 conditional novelty 6.0 of 10

    An enumeration algorithm for Type IIB flux vacua yields millions of explicit vacua in a two-modulus Calabi-Yau, exposing deviations from statistical predictions and a vacuum with |W0| about 5.5 x 10^-5.

  4. Finiteness and the Emergence of Dualities

    hep-th 2024-12 conditional novelty 6.0 of 10

    Finiteness of quantum gravity amplitudes implies moduli spaces have at most Euclidean volume growth, which in turn implies duality groups act semisimply on charge lattices.

  5. Uplifts in the Penumbra: Features of the Moduli Potential away from Infinite-Distance Boundaries

    hep-th 2024-12 conditional novelty 5.0 of 10

    In the crossover region between the moduli-space interior and strict asymptotic boundaries, the flux potential of one complex structure modulus admits de Sitter uplifting minima and axion valleys with flattened potentials.

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