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arXiv · 1910.09550

Exact $\beta$-function of Yang-Mills theory in 2+1 dimensions

Paul Romatschke
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Abstract

To set the stage, I discuss the $\beta$-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 $\beta$-function to the expectation value of the action in lattice gauge theory, and the latter to the trace of the energy-momentum tensor, I show 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 $\beta$-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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Paul Romatschke. 2019-10-21. Exact $\beta$-function of Yang-Mills theory in 2+1 dimensions. https://doi.org/10.1007/jhep03(2020)174

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