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

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.

12 pages, no figures; comments & criticism welcome

References in corpus (4)

• Correlations of Energy-Momentum Tensor via Gradient Flow in SU(3) Yang-Mills Theory at Finite Temperature
• Analytic Transport from Weak to Strong Coupling in the O(N) model
• Renormalization Scheme Dependence, RG Flow and Borel Summability in ${\varphi }^4$ Theories in $d<4$
• Finite temperature CFT results for all couplings: O(N) model in 2+1 dimensions

Cited by in corpus (2)

• Classical and Quantum Computing of Shear Viscosity for $2+1D$ SU(2) Gauge Theory
• Emergent Hydrodynamic Mode on SU(2) Plaquette Chains and Quantum Simulation