Abstract
We analyze the renormalon diagram of gauge theories on . In particular, we perform exact one loop calculations for the vacuum polarization in QCD with adjoint matter and observe that all infrared logarithms, as functions of the external momentum, cancel between the vacuum part and finite volume part, which eliminates the IR renormalon problem. We argue that the singularities in the Borel plane, arising from the topological neutral bions, are not associated with the renormalon diagram, but with the proliferation of the Feynman diagrams. As a byproduct, we obtain, for the first time, an exact one-loop result of the vacuum polarization which can be adapted to the case of thermal compactification of QCD.
Highlights
On the other hand, non-abelian gauge theories on R4 are strongly coupled, and nonperturbative effects are notable
This problem appears in quantum mechanics, but there the divergence is caused by the factorial proliferation of the number of the Feynman diagrams. One finds that such divergence is cured by instanton-anti-instanton events [15, 16], and a priori has nothing to do with the renormalon problem. It was recently suggested in [17, 18] that IR renormalon ambiguity cancellation can be understood in terms of semi-classical instanton-monopole solutions appearing in the theory on R3 × S1, but which do not appear on R4
Since we show that no renormalons exist in this theory, the inevitable conclusion is that the singularity in the Borel plane due to neutral bions is associated with the proliferation of diagrams, rather than the renormalon
Summary
There are excellent reviews of renormalons on R4 [10, 11], we will review the renormalon problem in R4 for completeness. Our arguments will be heuristic, postponing a careful analysis until the section
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