Finite-complexity description of EFTs consistent with quantum gravity

Establish that any effective field theory that can be consistently coupled with quantum gravity admits a finite-complexity description in the framework of o-minimal structures, by demonstrating that its couplings, moduli spaces, and relevant data are definable with finite format in an appropriate o-minimal setting.

Background

The paper quantifies the complexity of effective field theories using effective o-minimal structures, focusing on Seiberg–Witten theory as a case study. The authors argue that local duality frames and patchwise descriptions yield finite global complexity for effective couplings.

Building on this evidence, they point to a broader principle within the Swampland program: EFTs that can be consistently coupled to quantum gravity should admit tame, finite-complexity descriptions. They explicitly formulate this as a conjecture, emphasizing the role of o-minimality as the language capturing such finiteness.

References

In a companion paper , we frame this observation in the context of Swampland program and conjecture that any EFT that can be consistently coupled with Quantum Gravity admits a description with finite complexity in the language of o-minimality.

— On the Complexity of Effective Theories -- Seiberg-Witten theory  (2512.11029 - Carrascal et al., 11 Dec 2025) in Section 6 (Conclusions)

Finally, chapter~\ref{ch:EFTcomplexity} develops a notion of complexity for effective field theories, extending the discussion of chapter~\ref{ch:complexityQFT}, and culminates in the conjecture that this complexity is finite for theories consistent with quantum gravity.

— Tameness and Complexity in Quantum Field Theory and Gravity  (2609.19262 - Vliet, 16 Sep 2026) in Part III preamble, Quantum gravity; Chapter III.9, “Swampland complexity”