Abstract
We compute the topological susceptibility of the SU(N) Yang-Mills theory in the large-N limit with a percent level accuracy. This is achieved by measuring the gradient-flow definition of the susceptibility at three values of the lattice spacing for N=3,4,5,6. Thanks to this coverage of parameter space, we can extrapolate the results to the large-N and continuum limits with confidence. Open boundary conditions are instrumental to make simulations feasible on the finer lattices at the larger N.
Highlights
The limit of large number of colors N has proved to be a fruitful tool in the study of SU(N) Yang–Mills theories [1]
One example is the Witten–Veneziano formula explaining the large value of the mass of the η meson in the chiral limit [2,3]
32π 2 μνρσ tr Fμν Fρσ the topological charge density. This formula can be given a precise meaning in quantum field theory by properly defining the topological susceptibility χ in QCD and in the Yang–Mills theory [4,5,6,7]
Summary
The limit of large number of colors N has proved to be a fruitful tool in the study of SU(N) Yang–Mills theories [1]. Exploratory computations with cooling techniques at large N have a long tradition on the lattice [9,10,11], with quoted errors for the topological susceptibility at the 10% level These results, reflect the short-comings of the techniques available at the time. At large values of N this makes it exceedingly hard to perform reliable simulations at small lattice spacings, since the number of updates needed rises dramatically with the inverse lattice spacing [10,13] This comes on top of the increase of the cost of the updates growing with N3, such that it cannot be overcome by a brute force approach. For each group the three lattice spacings simulated range from 0.096 fm to 0.065 fm with leading O(a2) discretization effects decreasing by more than a factor 2 in size This coverage of parameter space allows for a robust extrapolation of the results to the large-N and continuum limits. The extrapolations to the continuum and large-N limit, giving the final results, are presented in Section 4 before some concluding remarks
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