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Tame Embeddings, Volume Growth, and Complexity of Moduli Spaces
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Quantum gravity is expected to impose constraints on the moduli spaces of massless fields that can arise in effective quantum field theories. A recent proposal asserts that the asymptotic volume growth of these spaces is severely restricted, and related to the existence of duality symmetries. In this work we link this proposal to a tameness criterion, by suggesting that any consistent moduli space should admit a tame isometric embedding into Euclidean space. This allows us to promote the volume growth constraint to a local condition, and give the growth coefficient a geometric interpretation in terms of complexity. We study the implications of this proposal for the emergence of dualities, as well as for the curvature and infinite distance limits of moduli spaces.
Forward citations
Cited by 4 Pith papers
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Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape
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.
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