Abstract
We present results for Wilson loops smoothed with the Yang-Mills gradient flow and matched through the scale t0. They provide renormalized and precise operators allowing to test the 1/N2 scaling both at finite lattice spacing and in the continuum limit. Our results show an excellent scaling up to 1/N = 1/3. Additionally, we obtain a very precise non-perturbative confirmation of factorization in the large N limit.
Highlights
A well known problem when studying QCD, is the fact that the coupling g is in general not small at relevant energy scales
If the theory was solvable in the 1/N → 0 limit, results at the physical value of 1/N = 1/3 could be recovered as corrections in powers of 1/N, and in the case of the pure gauge theory which we consider in this work, the expansion is in powers of 1/N2
The fact that corrections to the large N limit are organized in a power series in 1/N2 can be obtained in perturbation theory using the topological expansion proposed by ‘t Hooft
Summary
A well known problem when studying QCD, is the fact that the coupling g is in general not small at relevant energy scales. Several lattice collaborations have found agreement with scaling at a non-perturbative level [2, 3] The precision of these studies was mainly limited for two reasons. Second the problem of a bulk phase transition at intermediate lattice spacing and topological freezing at small lattice spacing are more and more severe at larger N and make it difficult to reach the continuum limit[4] We overcome these difficulties by using 1) high precision results for smooth Gradient flow observables and 2) open boundary conditions [5], extending the analysis of [6] to several observables. The latter has been of considerable interest in the lattice community, as it implies that theories at larger N can be simulated in smaller boxes, reducing the computational effort. We will verify factorization non-perturbatively and with high precision
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