Abstract
We measure the running of the SU(∞) ’t Hooft coupling by performing a step scaling analysis of the Twisted Eguchi-Kawai (TEK) model, the SU(N) gauge theory on a single site lattice with twisted boundary conditions. The computation relies on the conjecture that finite volume effects for SU(N) gauge theories defined on a 4-dimensional twisted torus are controlled by an effective size parameter \( \tilde{l}=l\sqrt{N} \), with l the torus period. We set the scale for the running coupling in terms of \( \tilde{l} \) and use the gradient flow to define a renormalized ’t Hooft coupling \( \lambda \left(\tilde{l}\right) \). In the TEK model, this idea allows the determination of the running of the coupling through a step scaling procedure that uses the rank of the group as a size parameter. The continuum renormalized coupling constant is extracted in the zero lattice spacing limit, which in the TEK model corresponds to the large N limit taken at fixed value of \( \lambda \left(\tilde{l}\right) \). The coupling constant is thus expected to coincide with that of the ordinary pure gauge theory at N = ∞. The idea is shown to work and permits us to follow the evolution of the coupling over a wide range of scales. At weak coupling we find a remarkable agreement with the perturbative two-loop formula for the running coupling.
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ArXiv ePrint: 1412.0941
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Pérez, M.G., González-Arroyo, A., Keegan, L. et al. The SU(∞) twisted gradient flow running coupling. J. High Energ. Phys. 2015, 38 (2015). https://doi.org/10.1007/JHEP01(2015)038
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DOI: https://doi.org/10.1007/JHEP01(2015)038