Finite specifiability of the ultraviolet formulation of QFT

Determine whether the small-distance (ultraviolet) formulation of realistic quantum field theories is finitely specifiable, specifically whether the bare Lagrangian requires an infinite number of irrelevant terms or admits a finite closed-form description.

Background

The paper discusses that non-renormalizable theories at the smallest scales may require infinitely many terms, raising concerns for reductionists who prefer a finite supervenience base. Even for renormalizable theories, structural features imply infinitely many possible irrelevant terms that could become significant at small distances.

Given current understanding, it is not established whether realistic QFTs at the smallest scales are finitely specifiable. Resolving this would clarify whether an ultraviolet finite basis exists or whether an infinite specification is necessary.

References

To be clear, my intention here is not to suggest that because we are currently unable to determine whether or not the small-distance theory is finitely-specifiable, we should conclude that the large-distance theory must be fundamental: that would be to mistake a limitation of our present epistemic access for a fact about ontology.

— Quantum Field Theory and the Limits of Reductionism  (2407.20457 - Adlam, 2024) in Section 3.3, Finite supervenience base

In our system, it remains an open problem whether the UV scheme dependence reflects the presence of infinitely many parameters, or a finite set of combinations would effectively suffice to determine the dynamics, thus restoring the predictivity.

— Can we make sense out of negative kinetic energy?  (2610.10040 - Maiezza et al., 7 Oct 2026) in Section 5, Comparison of regulator schemes