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

• Main Author: Paul Romatschke
• Format: Article
• Language: English
• Published: SpringerOpen 2020-03-01
• Series: Journal of High Energy Physics
• Subjects: Lattice field theory simulation; Non-perturbative renormalization
• Online Access: http://link.springer.com/article/10.1007/JHEP03(2020)174

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 d ln g 2 / μ d ln μ = − 1 $$ \frac{d\ln {g}^2/\mu }{d\ln \mu }=-1 $$ 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.