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.