It is common that quantum field theories are conceived incompletely (often as nothing but Lagrangian densities) and as such require further completion of their definition.
There are broadly two sectors that require special attention in this regard, concerning the definition and dynamics of quantum fields: at very
large length scales: “in the IR”,
where this jargon is a historical echo of the fact that:
ultraviolet (UV) light has small wavelengths,
infrared (IR) light has large wavelengths
compared to visible light.
But the length scales involved in UV/IR completions of quantum field theories are usually many orders of magnitude away from the wavelengths of visible light, in either direction, often to the extreme that:
UV-completion aims at the Planck scale,
IR-completion aims at cosmic scales.
At the same time, neither term is reflected much in the literature at all, nor even well defined, even by physics standards. The term “UV completion” is prominent in informal discussion of quantum gravity, where theories like string theory (not themselves QFTs!) are advertised as providing UV-completions of gravitational and gauge field theories . The term “IR-completion” has not been used much at all; but see the references below
One fairly precise use of the term “UV-complete” is in the sense of asymptotic safety, hence in the sense that the renormalization group flow of a perturbative quantum field theory never diverges in the direction of smaller length scales. The authors CLPPR 2014 use the term “IR-completion” (somewhat implicitly, after their equation (9)) in the same sense but sign-reversed sense, for RG-flows to large length scales.
However, this is far from being the universally accepted meaning of the term(s). Indeed, string theorists — probably the largest group of users of the term “UV-completion” in informal writing — typically claim both that string theory provides UV-completions and that this is incompatible with asymptotic safety (see there).
An evident part of the terminological problem is a glaring conceptual gap in quantum field theory: Precisely defined and nontrivial examples of complete QFTs in any sense of the word — the topic of constructive field theory — are notoriously elusive (cf. the Yang-Mills mass gap millennium problem) and this situation only becomes worse when going beyond the scope of QFTs into string theory (cf. the M-theory conjecture).
Indeed, there are structural completions necessary in QFT beyond the topic of RG-flow:
…
Already classically, the definition of (higher) gauge fields requires completion when their spacetime domain extends of a single coordinate chart to topologically non-trivial domains: This is the topic of flux/charge quantization and since it concerns the completion of the field content on the entirety of spacetime, it is global completions and hence arguably deserves to be filed under IR-completion.
A rare example of an article going beyond just dropping the term, by philosophers of science:
The usual folklore verbiage used in string theory appears in the abstract of:
“Abstract: One of the main goals of theoretical physics is to describe physics at all energy scales. The usual renormalization scheme of quantum field theory provides a way to investigate the details of physical systems at different energy scales, potentially up to some energy cut-off. When a theory is predictive at arbitrarily high energies and hence the cut-off can be removed, we say the theory is UV complete. The importance of UV completeness lies in its ability to explain physical phenomena at arbitrarily small distances or high energies. However, when standard techniques from quantum field theory fail to provide such a description, new degrees of freedom are expected to become important. In this thesis, we investigate two types of UV completions; one associated with conformal field theories and the other with quantum gravity. For the former, we study the fixed points of the renormalization group where one needs to integrate-in light solitonic particles/strings in the context of supersymmetric conformal field theories. For the latter, we review the challenges of UV completing quantum gravity and the severe constraints that such a completion is expected to provide for the low-energy physics. […]”
See also:
On IR-completeness as the sign-reversed form of asymptotic safety, concerning unbounded RG-flow to large scales:
On the global definition of higher gauge fields as a form of (classical, already) global and hence IR completion:
Last revised on November 8, 2026 at 16:25:59. See the history of this page for a list of all contributions to it.