Conjectured link between UV renormalons and Haag’s theorem

Establish whether ultraviolet renormalons in renormalized perturbation theory can be reinterpreted as manifestations of neglecting Haag’s theorem’s no-go result; specifically, prove that the presence of UV renormalons indicates a failure of self-consistent perturbative renormalization attributable to ignoring Haag’s theorem.

Background

Ultraviolet renormalons cause factorially divergent series and ambiguities in Borel resummation, traditionally viewed as genuine non-perturbative artifacts arising from renormalization. The paper argues that in their multifractal spacetime framework, both UV renormalons and UV Landau poles disappear, supporting the viability of perturbation theory once Haag’s theorem is circumvented via non-translationally invariant vacuum states.

The authors explicitly state a conjecture linking renormalons to the neglect of Haag’s theorem. They suggest that renormalon ambiguities reflect a failure of self-consistent perturbative renormalization tied to the no-go result of Haag’s theorem. Their framework provides supporting evidence by eliminating renormalons when the conditions enabling Haag’s theorem are violated, but a formal proof of this reinterpretation remains outstanding.