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DOE OSTI · 1803189

Exact β-function of Yang-Mills theory in 2+1 dimensions

Romatschke, Paul
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Abstract

To set the stage, I discuss the β-function of the massless O(N) model in three dimensions, which can be calculated exactly in the large N limit. Then, I consider SU(N) Yang-Mills theory in 2+1 space-time dimensions. Relating the β -function to the expectation value of the action in lattice gauge theory, and the latter to the trace of the energy-momentum tensor, Is how that $ \frac{d\ln {g}^2/\mu }{d\ln \mu }=-1 $ for all g and all N in one particular renormalization scheme. As a consequence, I find that the Yang-Mills β -function in three dimensions must have the same sign for all finite and positive bare coupling parameters in any renormalization scheme, and all non-trivial infrared fixed points are unreachable in practice.

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Romatschke, Paul. 2020-03-30. Exact β-function of Yang-Mills theory in 2+1 dimensions. https://doi.org/10.1007/jhep03(2020)174

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