PoS - Proceedings of Science
Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation
Determination of the continuous $\beta$ function of SU(3) Yang-Mills theory
C. Peterson*, A. Hasenfratz, J. van Sickle and O. Witzel
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Pre-published on: May 16, 2022
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In infinite volume the gradient flow transformation can be interpreted as a continuous real-space Wilsonian renormalization group (RG) transformation. This approach allows one to determine the continuous RG $\beta$ function, an alternative to the finite-volume step-scaling function. Unlike step-scaling, where the lattice must provide the only scale, the continuous $\beta$ function can be used even in the confining regime where dimensional transmutation generates a physical scale $\Lambda_{\mathrm{QCD}}$. We investigate a pure gauge SU(3) Yang-Mills theory both in the deconfined and the confined phases and determine the continuous $\beta$ function in both. Our investigation is based on simulations done with the tree-level Symanzik gauge action on lattice volumes up to $32^4$ using both Wilson and Zeuthen gradient flow (GF) measurements. Our continuum GF $\beta$ function exhibits considerably slower running than the universal 2-loop perturbative prediction, and at strong couplings it runs even slower than the 1-loop prediction.
DOI: https://doi.org/10.22323/1.396.0174
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