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  • Open Access

Tame embeddings, volume growth, and complexity of moduli spaces

Thomas W. Grimm, David Prieto, and Mick van Vliet

  • Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands

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Phys. Rev. D 112, 106015 – Published 24 November, 2025

DOI: https://doi.org/10.1103/d51c-j1s9

Abstract

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.

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Phys. Rev. D 112, 106015– Published 24 November, 2025
  • Received 24 June 2025
  • Accepted 28 October 2025
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