UV completion is procedure of extension of initial theory, which describe only low-enegry degrees of freedom of theory, to arbitrary energy scales. UV complete theory is one whose correlation functions or amplitudes may be calculated and yield unambiguously finite results for arbitrarily high energies.

We start with consider a non-renormalizable theory. As I understant, there are two concepts of UV complition:

  1. Wilsonian UV completion -- The standard (Wilsonian) approach to the problem is to build a UV-completion by integrating-in some new degrees of freedom that reconstruct a weakly coupled quantum field theory above the scale.

  2. Non-Wilsonian UV completion -- such modification cannot be obtained by integrating out heavy degrees of freedom

I am now try to understand some basic comcepts of Non-Wilsonian UV completion and know only two references where such completion was disscused: UV-Completion by Classicalization and Non-Wilsonian ultraviolet completion via transseries.

As I understand, existance of such Non-Wilsonian competion in some sence is the signal of incomletnies of Wilsonian RG. So I have following related (in some sence the same) questions:

  1. What may be wrong in Wilsonian concept of renormalisation?

  2. Which approaches may replace Wilsonian RG procedure?

  3. How intuitively understand possibillity of non-Wilsonian UV completion?


1 Answer 1


What may be wrong in Wilsonian concept of renormalisation?

It is known that some theories cannot have a standard Wilsonian (ie, weakly coupled) UV completion.

Here are some references:

[1] https://arxiv.org/abs/hep-th/0602178

[2] https://arxiv.org/abs/1601.04068

[3] https://arxiv.org/abs/1710.09611

Which approaches may replace Wilsonian RG procedure?

You listed some in your answer, e.g., classicalization.

How intuitively understand possibillity of non-Wilsonian UV completion?

As a logical possibility, it is not so hard to imagine a non-Wilsonian UV completion. In the effective field theory approach, the effective field theory breaks down at some scale $\Lambda$ where the infinite tower of irrelevant operators need to be resummed. The Wilsonian picture is that the correct UV theory that replaces the low energy effective field theory, is itself another weakly coupled field theory. "Non-Wilsonian UV completion" just means that "something else" replaces the low energy theory in the UV.

In the specific example of classicalization, the idea is that non-perturbative intermediate states appear in scattering amplitudes which restore the unitarity that is lost when you reach the cutoff scale $\Lambda$. For instance, in gravity, black holes can be formed as intermediate scattering states, and analogous non-perturbative classical states can appear in theories which may exhibit classicalization. There is some circumstantial evidence that these states can restore unitarity, discussed in the papers.

The difficult part is implementing this idea in practice. Wilsonian UV completions are the theories we know how to treat rigorously (at least a physics level of rigor). Non-Wilsonian UV completions are speculative, and as yet no one has an example where computations can be done in full detail to prove the scheme works.


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